Why does my PC randomly turn off by itself on startup?

First off, I wanted to say that I doubt very highly that this is heat related, my PC (even overclocked) idles at 35c. My system is below:

-Intel Core i5-750 Lynnfield (2.66ghz) @ 3.90 ghz
-GIGABYTE GA-P55M-UD2 Intel P55 Micro ATX Intel Motherboard
-SAPPHIRE Radeon HD 5770
-4GB DDR3 1600 Memory
-Corsair H50 CPU Cooler
-Antec 902 Case

Sometimes when my PC reboots, during the boot process (and sometimes as Windows 7 is loading) it shuts off. Usually after a few tries (especially if I back off on the overclocking) it will stay on, but it definitely bothers me and I'd like to get to the bottom of it.

Could this be caused by too low a core voltage? I believe mine is at 1.375...

Thanks very much.

 

What power supply?

 

600 watt.

It's run great for most of a year, no problems.

 

Just an update, I think the problem was a loose power cable going into the PSU. I seated it more firmly and the problem hasn't repeated. Thanks all...