I would guess it is a over heating problem and/or a faulty power supply. Monitor your cpu and video card temps before you run the game and then again a few minutes after before the computer shuts down.
I also agree you could try downloading OCCT and run 1st the CPU test then the GPU test it monitors the temps and stresses the components. You could also run Memtest if you think its not the PSU or overheating. What PSU do you have?