Dave, What make/output is the power supply? What is the consumption of the PC? How many hard drives, how much memory, any extra cards etc?
I had a very similar problem with my wife's PC about a year ago. Tried all sorts of things including a number of power supplies. It wasn't until I fitted a good quality 700watt power supply that the problem went away. Seemed like total overkill for the PC but it's been very stable ever since.
You should be able to find out what temperature the CPU is running at. Have you done this? The mobo manufacturer usually supply some sort of monitor program.
One program that might help identify the problem is Passmark Burnin Test. It's a very good stability test program.