(for the case that it doesn't continue to work properly)
Hi PHeMox,
I recently had very similar issues on my system (grafics: msi geforce 7900Gs). Problems sometimes vanished for a few days and returned then anew. At last nothing woorked anymore. I bought another grafics card in the end, but it wasn't the card, but the pciExpress on the mainboard that didn't work properly so I also bought a new mainboard (pwoer wasn't the problem). However I did a lot of researches as I had grafic problems with the new system as well at first:
1: Have you CCC installed and vpu recover activated? I had black screen when beginning to play grafic intensive games, however when activating vpu recover the grafic device will be reset and the game closed with an error (that's better than a complete crash). I could solve this issue by downclocking the grafic clock. That's not that nice but you could give it a try (you can use the CCC for that). First try it with a high amount (-100Mhz) when it works you can find the highest clock that works correctly (in my case that are -30Mhz, as the card is overclocked by company by 80Mhz that's not as bad).
2: Try another PCIE card for checking whether it's a mainboard problem.
3: If your ATI-card isn't published by ATI itself but by another company (ASUS, SAPPHIRE,MSI,...) go to their sites and check whether they have their own drivers (at least ASUS has them). That's important because different companies may build in different cooling systems on the card that might don't run properly with the native ati drivers.