I have abandoned games for the two following reasons:

#1 Not fun at all.
#2 Not my kind of game.

Other times, I will postpone playing a game that requires too much effort to play (learning curve is too high) and it might end up overlapping with #2 into revealing that, after all, it's not my kind of game. Some other times I will postpone playing a very hard game like Ghouls and Ghosts, but I will never give up on it completely.

One game I forgot was Skyrim because of the silly reason I couldn't decide what class to play :/ Started it many times but decided that it may be better to play another class.

The only games I'm bent on finishing are point & click adventure games, it nags me to leave those unfinished. For other genres I leave the majority of games unfinished. Especially grindy games like Pixeljunk Monsters that are fun for a while but would take a serious amount of repetitive tedious gameplay to complete without offering enough new content or excitement. When it's no longer fun, that's the exit visa. If a game fails to entertain me (and it will if I can't finish it) then any compulsive feeling about wanting to finish the game is the bigger problem than the fact that I didn't finish it. I must therefor work on myself more, to care more about things worth caring about and care less about things less worth caring about.
Any pimplefaced 14 year old can 100% a game without having achieved anything noteworthy in the world outside gaming so one can conclude from this that finishing a game isn't likely to bring enlightenment upon you or level you up as a person. It's just pushing around digital zeros and ones which is perfectly fine if you're having fun but it shouldn't become an obligatory mission.

Every time I catch myself wanting to finish a game, I realize that it's just a distraction from something more worthy/important that needs doing but it's easier to get a feeling of reward from a game. When a game is too hard/obtuse then it makes no sense to continue because you'll not get that quick feeling of reward you're seeking and you'll end up only wasting time getting nothing at all out of it.

Suffering through a plateau or difficulty spike is worth it for other skills and endeavors in life because the pay-off and true satisfaction are more lasting than the quickly evaporating feeling of achievement when you finally beat a tough game.

I'm trying to think what games I effectively gave up on, due to difficulty. Ignoring the plethora of such games from the nes and early dos era, three come to mind:

- MAX - Mechanized Assault and Exploration
I don't think I ever actually finished a level. I know I couldn't get past the first campaign level, so I ended up spending almost all of my time with the game playing skirmish matches, but I never finished one. That is, I never defeated the enemy during a skirmish. Not that it was too difficult to manage, it was simply too much fun building a big powerful base. The campaign on the other hand was tough as nails, and I didn't see any way of getting past the first level. Granted I was young, so perhaps I should try again.

- SWAT 3
Got to the last level, where you had to wipe out terrorists with armed nuclear device at an airport. Awesome level, but too difficult. The last of them was in the control tower, but I simply couldn't get in there without getting wiped. I'm sure you could throw a flashbang in, only you have to throw it in a certain way, but seeing as you can't save during a level (from what I can remember), and since it took a long time to fight your way to the tower, I eventually gave up. Rainbow six is way easier :P

- Syndicate Wars
The blasted space station level, but not because it was too difficult. The problem with that level is that any explosion anywhere instantly results in a mission failure since the entire station blows up. Compounding this issue is the fact that several of the enemies carry bombs, which automatically activate when they die, and to disarm one you need to pick it up within a couple of seconds. Unfortunately there is some bug/technical issue with that level that causes your agents to sometimes flat out refuse an order to pick up a bomb, even if they have inventory space available. Again, you can't save mid level, and seeing as there's about a 50% chance of picking up a bomb and there are 10 or so bombs through the level, I quickly realized that there was almost no way that I could finish the level. It's the second to last level as well, which made it extra agonizing :P

What do I intend to do with them? I suppose I'll retry the first one, but I don't imagine I'll try the latter two again.
Ugh....yes I remember that fight. It was hands down the most difficult fight for me of the series. It's from Two Thrones: https://www.youtube.com/watch?v=c8bOw6Hvl2I

Yeah, that is the game. Still wondering if this fight was meant to be that hard.

Depends on whether or not I enjoyed the game up to that point. If a game has me hooked then I'll figure out a way to get through. If it's so-so but I'm near the end, I'll also figure out a way. If it's meh and I haven't gotten far, I'll move on to other games without much of a look back.

Examples: BG2, was getting near the end but the combat was getting ridiculous and I wasn't having much fun. But I was in the final areas, had put in a lot of time to get that far, and just had to see it through. Cheat-code kills solved that problem.

Panzer General 2, wasn't far along, maybe the fourth scenario. Wasn't enjoying it that much and I wasn't able to beat the scenario. After a few tries I decided to move on to some other game. It reinforced my dislike of scenarios with time or turn limits.

I never play more than one game at once. I treat games like books or films and give each one of them their time and respect.

For the last 2 years I try to beat Thief's Return to The Cathedral level every once in a while but I just can't beat that annoying crap of level in an otherwise great game. I feel really bad for playing other games because I am still "officialy" playing Thief.

And I hate it.

I think that it's mostly a problem with brand new games. There are exceptions like Diablo 2 where Blizzard kept on patching it for many, many years after the fact, but I'm not sure how many of those affected save games.

Anyways, I doubt that it's a common problem and in most cases you can just choose not to apply the update.

Backing up game saves. Hmmm, that's an interesting idea. Not that I'm every going to use it, but still thanks for the idea.

Like others said. Save and wait for a better day, cheat, or just uninstall.

I will always try to beat a game even if playing the game isn't fun. It is a personal flaw. If a game isn't fun, for one reason or another, the best solution would be to just drop the game and move on, and there are times when I have done that, but I will always try to beat the game.

It has been a while since I have given up on a game, but back in the days of Nintendo, I had more than a few games amassed that had been left unbeaten and collecting dust; then the Game Genie came out. I don't like cheating, but the Genie allowed me to go back and breath some fresh air into garbage titles like Rambo and Predator... I had a lot of bad games back then...lol

Years ago I used to have a somewhat OCD-like urge to beat games even if I didn't enjoy them (perhaps as a challenge of some sort), but that is behind me. There are usually better ways to waste time. I think the last game I threw away was Redneck Rampage. I don't miss it a bit.

If it's a game I like I put it off to the side and get back to it at a later point (did that with Catherine, Dishonored, and a few others). If it's a game I hate or have no interest in I just uninstall it/get rid of it (Dead Island, Sonic 2006, etc.).

If it`s tough, I`m a stubborn old fecker & will stick at it, even whilst turning the air blue.
If it`s just some puzzle where you have to search online for the answer & then think "who the hell would ever of got that!? o0", then I ragequit & it gets left to one side for ages.

Some though, I just can`t play because they`re awful. Big fan of Magicka (even though buggy) & completely nuts for Magicka Wizard Wars, so when magicka2 was coming out, new pants please!!

Bought the pre-order (bonus robes for MWW \o/ ), played day of release.
It sucked big time (polite version). It got left on HDD for further "fixes/patches", which didn`t make it much better.
New hdd installed, folks from MWW bought it in recent sale & wanted to co-op, but I still refuse to touch it lol