Im currently using a 6950 2gig and i have been having the dreaded "Display drivers have failed and recovered" Error and occasionally a BSOD. I havn't had an error in a while since I updated to the 12.6 Beta drivers but i've been seeing the occasional frame drop in games that shouldnt give it any problems, such as League of Legends. Some games have caused my display to freeze making me restart my system. I don't think it is a driver issue anymore, I think it has something to do with my psu. Before I upgraded to my 6950, I was using an 8800gt with the same psu and was having the same Display drivers have failed and recovered error.
I was having that prob with my card as well which is a gtx 560 sc, i am not an expert but for me it was just the drivers i was using so i downgraded them till the new ones came out. and now it has not happened since
I used to have almost the same exact problem as you have. This might have no relevance at all and might not fix it, but this was my solution.
So way back when I first built my computer, I had a 965BE, similar to yours, and a 2GB 6950. Ran fine for awhile. Then this "display drivers has failed" error started to come up. I figured it was the card, since I had tried all drivers and stuff. Then, my friend upgraded his 8800GT, and I thought I would just use that until I could find out what the problem was. Turns out that was not the case.
I slaved for hours over what the problem could possibly be. One day, while staring at the components of my system, I figured I may as well try everything, and took out 2 of my 4 sticks of RAM, and PRESTO, it worked.
Anyway, I'm not saying that the RAM is the problem, I'm just saying investigate everything. It could be an overclock, or even a power supply issue.
did it start before you started using the beta drivers? if it didnt roll them back to older drivers if not i definately wouldnt put it past your psu not being 80+ rated its gonna lose 20+% of its power to heat and waste and i havent used bfg's so i dont know what the quality is like either, but yeah when i have had psu's failing over the years i have had frame rate issues and crashes