You say that it shuts down as if you yourself shut it down. Do you mean that it goes through the whole process of logging off ect, or does it simply go black? Or does it do some funny thing like stall for about 5 seconds, quit orbiter and display the background, then go black?
I agree with Lingo. Open up your computer, check and remove dust, make sure the fans and everything are all working, and try to maximise air flow (by tying cables together, ect). Be sure that you have heat sinks where they are needed.