^+1 Your CPU might be overheating.
I did have the same problem with my newest PC a while ago. I thought it was the PSU (had a 550W). Got a 800W (which blew out from a brown out) and same thing. Temps were fine.
In my case it turned out that the mobo was setting the memory voltage and timings wrong. Had to set them manually. Once I did that it was all good.
Might want to check that out in your BIOS.