OK, I have had a problem like this before with a system I did, and what I did is turned the heat sink around and it solved the problem, what it sounds like is that your CPU is over heating and the bios is doing an outa cut off to be safe, but it would boot back up.
Have you over clacked it in any way?
Also what processor do you have?
this idea of mine may not be correct, but really worth trying
