You didn't mention what OS you are running. If you are in XP, it is set to reboot automatically after a bad crash (i.e. resulting from a hardware issue). It doesn't even tell you it is rebooting, the screen just goes black and restarts. If you go into System>Startup And Recovery tab and uncheck the "automatically restart" box under the System Failure Options. Then, you'll get a proper bluescreen of death. If you get that, it is probably something not PSU related.
I ran into the same problem at the beginning of the year with my A7N8X-DX. My screen would go black, than it would reboot. I also had issues with it booting up from a cold boot, restarting a few minutes later and then running fine all day long after it was warmed up. Since WinXP just restarted itself without telling me it had seriously crashed (like all other prior versions of Windows), I at first thought it was the PSU not cold starting well and causing the system to hiccup.
It actually turned out that Asus' early BIOSes for my board had issues with my RAM. There wasn't anything WRONG physically with my RAM and it worked fine in other machines, but with the early BIOSes my nForce 2 board couldn't run the RAM 100% stable in Dual Channel mode. (of course, I was being cheap and not only forgoing the matched pairs, but using two different brands). Once I upgraded my BIOS to the 1004 version, my system has been solid as a rock (even with THREE different brands of RAM in my machine now). Maybe Intel is in the process of working out the same Dual Channel DDR issues that plagued the nForce 2's when they first came out. I do remember that for my board, there was a know issue with running Corsair XMS in DC mode. Maybe Corsair does something with their RAM that is not totally out of spec, but is just unique enough to throw off the board's ability to sync up the DDR timings. I haven't heard about any issues with the 865 motherboards, but a check on Intel's BIOS update page might help. (It is always a bit of a nail-biter to flash the BIOS on a board that isn't 100% stable though). I haven't played around with the 865 boards to know if you can do this, but it might be worth tyring to run on a single stick of RAM and see if it quits rebooting at random with the memory in Single Channel mode. That way, you might be able to isolate the problem, and hopefully stabilize the system enough to try out a newer BIOS.
Intel has a repuation for making good boards, but the only board manufactured by them that I've ever owned was a 815EEAL. Straight out of the box that board had MAJOR issues running a GeForce 2 MX in the AGP slot. Every game would lock up after a few minutes of play. It took me trying every other option before I went ahead and flashed the BIOS to the newest version, which wound up fixing the issue. So from my experience it is not unknown for even Intel to ship a board with a not-quite-done BIOS.