That game might use more memory than others you tried, or it might be more demanding for the gpu - to me, it still looks like a dying card. You could try to verify if it is the gpu by running furmark, but if it really is dying, this could be its death sentence. To check if it's the memory, you could try Fallout with the highres texture pack or something like that. If it turns out that it's just rainbow six, all the better, if not: The cooler the card, the longer it lives. So you'd maximize its life expectancy by not starting any games and let the fan blow stronger.