As I was shuffling through my finished games, both from retail and digital, a thought came to my mind. I was thinking that there were many videogame series in the last 20-30 years. Some of them were considered very important in gaming history, others not so. But MOST of them have stopped. What happened to them? In some cases their developers have ceased to exist. Others have been bought by other developers. But NONE of them deems it worthy anymore to continue the tale/series? I understand that in some of them, it was the last part in the series that received bad reviews from critics (and made low sales), but is it enough that ONE badly done (for various reasons) game to ruin the whole series? Couldn’t the developers say: “It was a mistake, OK. We’ll learn from it. The series continues”! I remember at some point (10-15 years ago) gaming magazines were writing “the developers don’t risk to make something new, they continue the same and the same series”! Why is that bad? Why not see the protagonist of a series to overcome a new difficulty in each game, becoming better and saving the day, and we are growing (through the years) with him? And now we don’t have even that! I’m mostly talking about the series(es):

Max Payne
No One Lives Forever
Alone in the Dark
Earth 2140-2160
Two Worlds
Sacred
Soldier of Fortune
Thief
Neverwinter Nights
Dungeon Siege
Styx
Gothic(s)
Risen(s)
Project I.G.I.
The Longest Journey (or Dreamfall)
Dracula (adventures)
Half-Life (of course!)
Gabriel Knight
Serious Sam
Painkiller
Warcraft (single player)
BloodRayne
Crysis
Torchlight
F.E.A.R.
Prototype
Dirt (Colin McRae rally games)
Dishonored
Secret Files
Broken Sword
Lost Horizon

And I surely forget others.

Whereas series continuing (with more or less often new games) are:

Tomb Raider
Hitman
Syberia
Age of Empires
Divinity games
Far Cry
Deus Ex
SpellForce
S.T.A.L.K.E.R.
Assassins Creed
Doom
Elder Scrolls
Witcher
Call of Duty
Layers of Fear
Homeworld
Darksiders
Fallout
Grand Theft Auto

And as I revise the second list, I think that some of them could be put in the first one as well, as sufficient years have passed since their last game.

I surely would like to see Max Payne, Master Thief Garret, Nina Kalenkov, Cate Archer, and others again...

Well, at least those games were somewhat succesful enough to spawn sequels.
There were also games, which critically were very good that never got the sequels they deserved.
Games like Anachronox and Legendary for example, but there are more.

You partially answered your own question already.

- Licensing issues (how can anyone make a new Kate Archer game with the legal situation so complicated that not even the classic games can be sold anymore?)

- Commercial failures (the AAA industry is very risk-averse) and the dilemma that you can't win: if you aim to mimick the classics, reviewers will say you're unoriginal, if you try something new and different, fanboys are bound to throw fits of rage over it.

- Some franchises might not fit the times that well anymore. I can't see anyone in the AAA industry doing something bold like Neverwinter Nights again these days, a powerful but easy-to-use tool for players to create their own free entertainment with, plus host their own servers without any monetization - we're lucky they managed to get this greenlighted even back then. Sure, they could do an entirely different type of game with the "Neverwinter" tag on it. Oh, wait, that was done already - it was a MMO which is now F2P. ;P

I'd say The Longest Journey/Dreamfall fits better in your second category, next to Syberia, as they did continue it many years later (but with mixed reception). And Piranha Bytes just changes the names from Gothic to Risen to Elex, but they're still more or less creating the same game. ;)

Besides, all stories have to end somewhere, and IMO it's better to let them end on a high note, before people get sick of them (see many TV series who overstayed their welcome and left a bad aftertaste). And the devs themselves might get bored after a while, too. The worst that could happen to Arkane Studios, for example, would be Bethesda stiffling their creativity and forcing them to just create one Dishonored game after another. (There would have been no Prey, no Deathloop etc.)

Leaving aside that sometimes it's better to think about a new story rather than rehashing an old world, for your ones above, I have a few comments. Not sure about the rest of the list, but these ones I knew without having to google.

NOLF - agreed, but it's in IP hell, so even if you wanted to make a new game you would have a hell of a time getting the rights sorted out

Thief - the last game was 2014, so not that long ago

Longest Journey - last game was 2016, so not that long ago

Half-Life - Half-Life Alyx released in 2020. Yes, it was VR only, so pretty niche, but apparently sold 2m units.

Serious Sam - Siberian Mayhem literally came out last year

Dirt - Dirt Rally 2.0 was released in 2019. Dirt 5 was released in 2021.

Gamers are always complaining about game series being milked to death and that newly released games lack innovations.

Now you ask why series x and y and z aren't continued.

Edit:
Many "last" games in series were the ones that did cost most in production (emboldened by the success of their predecessors), but then sold the least units.

Often due to offering either "too much of the same old" or "too much new stuff, that nobody asked for".
(notice the irony?)

So, of course, after such a negative experience, the developers (and even more so: the upfront financing publishers) did not invest even more time and money in those series.

Apart from that: how often have you heard someone say something stupid like "they ruined my childhood!", whenever a new iteration of an old, beloved game series didn't meet "the community's" (most probably overblown) expectations?
Or they added in-game transactions, or the new game got released on consoles first, etc...

The gaming "community" is never satisfied. There's always something "wrong".

Outside of Zombie flicks the motto is: what is dead, should better remain dead.

Two Worlds II got a bunch of recent DLCs and expansions (Shattered Embrace being the most recent, not on GOG), and there were talks of Two Worlds III, last word on a quick search was "not until at least 2022". That came and went, but it was "at least" after all. For a long time PB didn't have the Gothic IP anymore, which was why they made Risen. And that one rather drifted off I'd say, so they moved on to ELEX. In terms of core gameplay, they're mostly the same thing, just different worlds, so why not? And, while I think they were saying they were considering it when they recovered the IP, it'd be difficult for them to really continue Gothic, considering what happened in it after they lost the rights. Why would Blizzard bother? Not that major studios go for RTSs at all anymore anyway. Remasters...

What Leroux said is what my reply would be as well, licence and really bad sales and risk are the major factors of not receiving a sequel fast.

You should strike these games of your list though

Max Payne 1&2 will receive a remake by Remedy sometime in the future after Alan Wake 2
Alone in the Dark has a reboot in the works
Thief and Deus Ex will also receive sequels/remakes THQ nordic owns these games and have said they are interested in bringing them back
Styx 3 is also something we might see in the future, Cyanide studios has a game in the works that will have stealth in it
Gothic has a remake in the works
Project IGI Origins is a prequel to the main series
Painkiller will also be back (THQ Nordic)
Half-life had alyx a while back, who knows whats next but the ending of that game hinted that more is to come
Serious Sam had siberian mayhem a year ago, so its not dead
Bloodrayne had a remasterer a while ago, they are testing the waters for the future of the series
Crysis 4 has been confirmed by crytek
Dishonored DOTO only came out 5 years ago, arkane is busy with deathloop and other projects, so its not dead

Well, for some of them, it's easy.

Max Payne - 3 didn't live up to the legacy of the first two, killed the franchise.
Sacred - 3 was basically a mobile game released on PC, didn't live up to the legacy of the first two, killed the franchise.
Dungeon Siege - 3 was terrible and didn't live up to the legacy of the first two, killed the franchise.
Painkiller - any attempts to milk it after Overdose were massive failures, I really mean it when I say "Avoid Redemption and Resurrection as the plague". The Hell&Damnation version from THQ was also terrible compared to the original.

FEAR - again, the series got progressively worse until finally, FEAR 3 killed the franchise.
Warcraft - after the massive success that was WoW, it unfortunately lead to the death of hope for any single player Warcraft ever again. Can't really recover from the "MMOification" of the lore and story unless Warcraft 4 simply ignores everything that happened.

Soldier of Fortune - 2 was mediocre at best and the latest attempt - Payback - was so bad it most likely killed the franchise.

NOT DEAD:
Serious Sam - still around and kicking, not sure why you listed it.
Styx - Shards of Darkness came out in 2017 and was pretty good. Definitely wouldn't consider it dead yet.
Torchlight - definitely not dead. Torchlight Infinite came out in 2022.

More series you could add that got killed by a misguided sequel (the most frequent cause of death):
Command & Conquer
Duke Nukem

Agreed. I also don't consider those as a sign that a series is alive. More of a "Let's milk this IP one last time" kind of thing.

Remakes/remasters obviously are not a continuation of a series, the reason the are created is the see if interest still exists and if the risk of making a full blown sequel to a series that was dormant decades ago is viable and worth it, (the cost of something entirely new is MUCH higher) which is not a bad thing and a very smart business choice.

If a remaster/remake sells well enough the chances of an actual sequel are very high.

Personal opinion: I never cared for remakes (same story told different way, meh) and remasters 9 times out of ten are worse than the original and more buggy.

But as I mentioned above they do serve a purpose, they didn't jump pump it out like that, they are testing the waters

As others have said, sometimes it's rights issues, sometimes the games wouldn't fit (NWN was a good example of something that would be dumbed down (no toolkit) for the sake of "platform parity" and turned into DLC-spam if released today). Likewise, where did many old-school RTS's go? The whole genre got dumbed down into MOBA's. I wouldn't. Not flogging everything to death with endless remakes isn't always a bad thing though. Eg:-

- I value No One Lives Forever franchise more precisely because we had 2x really good games and not 18x Call of NOLFy's.

- Same with Thief, I'd rather remember the first 3x they did right than the 2014 buggy mess whose mechanics were a huge step back even compared to Thief 3 (screen flashes white in case you’re too stupid to use the light gem which itself was dumbed down from 11 to just 3 different detection states, etc). For more of the same content at "peak mechanics" of the first two games, there's a ton of decent mods out there.

- Age of Empires 3 was a step back vs AoE 1-2 (random generated maps removed).

- Further Dishonored and Deus Ex remakes were shelved precisely because the newest ones didn't meet sales expectations. Many, many other games you mentioned (eg, Broken Sword, Longest Journey, Syberia, Torchlight, Lost Horizon, FEAR, etc) to me peaked with the first 1-2 entries.

I feel you miss the point that back in the 90's-2000's many seemingly "abandoned IP" have been "sequelled" in the alternative way of creating something similar but new. Eg, if ID Software spent the 90's rapidly churning out Doom 3-6, Quake would not have been made. If Ken Levine had spent the 2007-2012 years spamming off System Shock 3-5, the Bioshock trilogy would not have been made. If Bioware had churned out Baldur's Gate 3-5 between 2000-2009, NWN and Dragon Age Origins would not have been made. If Ensemble had rapidly sequelled AoE 2 into AoE 3-5 during 2000-2002, Age of Mythology would not have been made. Studios (whose staff regularly work on more than one franchise) can make only so much in a given time period, and if a development team is tied up over-sequelling everything for 20 years, then who's going to make any new stuff?...

Because it gets incredibly stale. I don't mind a few sequels but some franchises have become literal "IP spam" where the protagonist isn't 'growing' at all but just exists for the sake of cheap marketing of cashing in on yesteryear. Many overly monetized games today are openly designed for investors rather than gamers. Not just for games either. A few years back I enjoyed a couple of super-hero movies, now I (and many others) are getting sick of hearing the word "Marvell". You can't keep flogging the same thing to death forever as a substitute for coming up with new ideas. Here's an interesting thought - if 1990's to mid 2000's game developers / publishers kept churning out sequels to 80's IP for +20 years the same way today's developers / publishers keep churning out sequels to 1990's to mid 2000's (Call of Duty, Far Cry, Tomb Raider, Battlefield, etc), many of those franchises you listed probably wouldn't have been created in the first place as everyone would have been buying Ultima 34, Paperboy 17, Frogger 23, Maniac Mansion 7, and Zork 57, well into the mid-2000's... I'm glad I grew up in that decade (90s) that had enough widespread "original ideas are a good thing" mentality to permit all those series you listed to be created in the first place instead of taking the cheap option of endlessly sequelling 80's stuff because it was 'safe for investors'.

Not if the mistake costs millions.

A lot of these series either had a poorly-selling last installment, weren't huge sellers to begin with (in a period where budgets were not ridiculously inflated), or were replaced by something else (Gothic by Risen, Risen by Elex and Warcraft by the far more successful World of Warcraft).

Some of these are close to, but not quite as silly as asking for a sequel to Earthworm Jim, Boogerman, or Advent Rising.