playing sky'rim atm with a 5870 and the game works fine for me.
normally if the screen blanks and restarts the drivers you need to reinstall them as they can become corrupted over time. it can also be caused if you didnt update the direct x with the version that comes with the game.
1 last thing. if the vrm gets to hot it can cause the card to go to sleep causing the driver to quit. but if this happens the driver wont restart. so its unlikely to be a vrm issue.