The game's interface buttons will randomly turn black (see attached screenshot). It's not always the inventory button, it happens with any of them. It's also not just a case of the texture not loading because clicking the black area where the button is supposed to be doesn't work. I generally use the keyboard shortcuts, so it's not a big deal, but it just bothers me seeing them. Saving and reloading doesn't fix it, and it even persists no matter what save I load. Restarting the game is the only thing that fixes it. I haven't noticed a pattern either. Sometimes i can play for hours and it never happens, and sometimes it happens a few minutes after starting and does it several times in a row after restarting the game.

I don't recall having this problem before. I searched here and only found results for black screen. I tried my Google-fu, but I only get pages of crap about "Fallout" 4. I wonder if it's something with the latest version of the high res patch (4.1.8), just rare or buried deep in the search results. I hope it's not a sign of save game corruption because it seems to be happening more often now than when I first started.

Does anyone know what's causing it or how to fix it? I'm using the high-res patch and TeamX 1.3.5. I've configured the high res patch to run at 1080p with x2 scaling in full screen windowed mode.

It was in "vanilla" version too (including official patches). Try FIXT:
http://www.nma-fallout.com/threads/fallout-fixt-0-81alpha-july-5th-2015.194562/

Don't use other fixes and patches because FIXT got it all. During install you can choose how much it can be "fixt" - only unofficial patches patches or "restored content" too.

And there is something with lack of compatibility with saves so... you were warned! ;-)

I don't remember it happening in pure vanilla 1.2 or the last time I played using TeamX 1.2.x without the high res patch a long time ago. I didn't use the high res patch then because I had a different monitor and didn't like the higher resolutions because it zoomed out and made it hard to see items laying on the ground. I've used the high res patch several years ago after getting a 1080p display since running 1080p with x2 doesn't zoom out too much, but i didn't finish that game and it didn't happen during the time I did play.

I've know about Fixt and plan to play it one day if it gets finished, but I'm not even going to try switching "patches" this far into the game. The saves will mostly likely not be compatible and I'm not starting over when I'm about 3/4 of the way through the game.

Well... you can try Sfall for Fo1 but I don't remember if old saves will work after this:
https://github.com/Sduibek/sfall_1

http://www.nma-fallout.com/threads/fallout-1-lots-of-new-features-with-unofficial-sfall-release.203378/

FIXT has it already but it's more "complex patch".

I know what causing it (at least I'm almost sure), but don't know how to fix it. Whatever recommended patch I used, never helped.

The cause of this are too many entries in the PipBoy (entries, as in when you download data from holodiscs, not quest list). This, as I understand it, causes some glitches in game engine. If I recall correctly, though I may be wrong, if you have more than 13 entries, game begins to glitch.
I don't think there are any solutions to this. :)

And it looks like there is solution for this - delete entries from PipBoy:
http://www.nma-fallout.com/threads/fallout-2-missing-red-skilldex-button.154973/page-2#post-3451448

Grab DAT Explorer e.g. from here:
http://fallout-corner.pl/download/fallout_1/narzedzia/f1-dat-explorer.zip

That seems to be the problem. I have exactly 13 (unless it can't display more than that). I just tested it by opening the PIP Boy Status page and and a random button disappears right after I close it. I hardly ever open that page, which is why I can usually play for hours and never have a button disappear.

If I'm reading the NMA post correctly, it seems to be just a graphical glitch and not related to the "too many items" bug in Fallout 2. I can live with it since I use the keyboard shortcuts already.