I theory you should be fine, i believe the recommended PSU for a single 5970 is 650w, and 850w for 5970x2. Unless, you actually have a piss-poor non-branded PSU you picked up for $30 at a flea market, which I doubt since you have invested in other valuable parts. I have to assume you know better than that, heh.
Perhaps you have a lower binned 5970 that doesn't take well to OC?
Perhaps it is a heat issue? GPU-Z is a free download for easy temp monitoring.
Have you installed the newest drivers from ATI, or running off the drivers included with the card?
Barring all other problems, if it is performing well at stock, but fails with OC, getting an RMA on the card could be problematic short of lieing, but might be the best option if OC'ing the card is essential to you.