The usual thing is to suspect the PSU (Power Supply Unit.). Even a very good PSU may be susceptible to sudden shutoff. So using a spare PSU is the normal way to test fort this kind of problem. Otherwise, it is very time-consuming to try and pin point the specific cause.
If the spare PSU does not eliminate the problem:
Use a different wall plug, even on a different circuit. **
Remove the DVD and see if the problem clears up.
Remove the hard and run it with Linux 'Live' CD..
Replace all RAM sticks with one spare RAM.
Replace the graphics card.
Of curse, the last thing is the motherboard.
** Rare, but faulty electrical system can do this.