You might try the 12.1a preview?
Just yesterday I finally got my dual-DVI HD5770 working in a rebuilt machine, and the initial 12.1
drivers that were installed gave me BSOD every 5 minutes. Could not operate the system to do anything.
I finally had to uninstall all ATI software, reverting to vanilla generic MS video support, in order to research the problem.
Found that 12.1 was extremely unstable for some, and that 12.1a solved the BSOD problem. Certainly couldn't hurt for me to try it... as 12.1 was unusable. In addition to
downloading 12.1a from the AMD site I even downloaded the 11.9 back-level
driver, in case 12.1a didn't solve my problem.
Anyway... it was like a TOTAL MIRACLE!!! Whatever was wrong with 12.1, it certainly has seemingly been fixed in 12.1a. Absolute rock-solid stability in my new machine with new HD5770 and dual-DVI 1920x1200 LCD monitors.
So you might give that a try, and see if it helps out in your situation.