I have two save states from different play attempts on the system now. At that point it re-launches the game and I'm sent back to the last hard save. The console isn't crashing or anything, I just open the save state screen when nothing is going on in the game, save state>load state>"load savestate failed".
I use save states frequently, but I've run into the issue twice were a save state I created moments ago will fail to load. I've been running Yu-Gi-Oh Tag Force GX on the 64-bit client, which runs very well for extended periods of time. Slightly different issue, didn't seem thread-worthy when this was open and recent. It's possible it's a bug, maybe you mean just the game crashes but you can restart it. However, the game is more or less popular, so I'd be surprised if other people had the same experience but no one else was reporting it. I don't have (or like) GTA, so I personally have not tested this. It sounds like this is only with GTA games, but you're not really being clear. Do you mean it crashes the first time you save state after restarting your computer or something? Or just if you leave it alone for a while? Those sound like potential problems with your computer or OS install, if so. If it crashes, the playing session is over. "It crashes just the first time in a playing session." To me a playing session is when the program is running. I don't really understand what you're saying though. Have you made sure you've updated your drivers? What card do you have?
If it happens with both backends, this doesn't really disprove the video driver idea. It's unlikely you're running out of that on a desktop, but if that number is like 2.0 GB, it could be the reason it's crashing perhaps (or if you have a lot of programs open and it's higher, maybe?) It's a situation we could handle better, although we typically only require ~128 MB to create a save state at most. If you right click on Computer and go to Properties, you should see "Installed memory (RAM)". Memory isn't the same thing as disk space. People bumping things without much useful info annoys me which ain't fun, so you'll understand if it makes me ignore uninteresting issues.
I personally just do this in my free time for fun.