Same problem here. I installed software to monitor temperatures - the card was quickly reaching 120 degrees within a few minutes of starting any demanding 3D game, and then shutting down shortly after. Found out it's got a shutdown switch to prevent it from heating above 130.
The stock cooling on the card is not sufficient and fails as the fans get a little older and more dusty. Solution is to add a good after-market cooling solution like either of these:
http://www.ncix.com/products/?sku=42005
http://www.ncix.com/products/?sku=48358
The card is still powerful enough to be worth this rather than replacing.
Cheers,
Paul