I have a long-time issue I can't figure out so I decided to ask for the common knowledge of the community to help me out.

I have a weird issue with certain games but I can't see any apparent pattern in it. Some games show this issue, some don't. When I start playing, everything works fine, then after some time the screen suddenly goes black, and the monitor goes into "off" state, like when I turn off my PC.
- It's not the monitor itself - I have my PS3 connected to it and if I switch channels it works fine.
- It's not the game, The game seems running, I hear sounds from the speaker.
- It doesn't seem to be RAM or CPU either because the PC works fine for other games.

My best guess is that the GPU has some issue but I can't figure out what, and I can't prove anything to use the warranty either.
It works perfectly for games like Witcher 3, For Honor, Stellaris, Project CARS, F1 Challenge, Star Trek Armada 2 (to list a few old games as well :P) but fails with Jurassic Park: Operation Genesis, Star Wars Empire at War, or The Crew 2 (both the Alpha and the Beta version).

But I made some stress tests (Furmark) and the GPU seemed to work fine... I made CPU stress tests as well, nothing strange there either.

The strangest thing is that sometimes I can play the games for a few minutes or even quarter of an hour, but sometimes the issue appear after a few seconds.

Any idea what could causing the problem or how to track it down?