As this happens after a few minutes of gaming, I somehow suppose the temperature in your case is getting too high to operate the system properly.
Although the GPU isn't really warm, there might be some other parts that can't take the heat. This can be the memory of the card, your CPU, your northbridge, your internal memory or even your PSU.
Besides heat, it could be that the PSU doesn't provide enough juice to make the system run stable...
If I where you, I'd open up my case and put a big fan next to it and set it to blow in my case at full speed... do some gaming and see what happens..
(ps: could you put some temp. information here? it may be a good idea to install a program like mainboard monitor and to enable the logging feature)