I been having that same issue with my hd6870 for sometime now Diamond is supposed to be RMA 'ing my card but i fear im going to just buy one myself
They are taking too long to respond and keep asking me for the same information they already been given time and time again
You can try the card in a different unit to see if it does it again but if it starts out doing the flickering etc it will just get worst
the best thing you can do is uninstall the ccc and let it ride with out it that will stop it from quiting and recovering mind you this will effect gpu perfromance and index score 3d and aero effects
That was the only way i found to stablize my card but it got to the point where it would BSOD on log on screen ,so i ended up taking it out and putting my old hd 5770 and it has been flawless since
im starting to think with all the issues people are getting with the hd6870 cards i think it might there programing of thiere new drivers or the cards are just lemons all the way around