I have the same issue, and it drove me nuts till I found this solution. I wish I had saved the URL for where I found this, but I will try and explain how I fixed it:
1) Create a profile in Catalyst Control Center and give it a name. Call it "Test" for this example.
2) Open your "Test" profile with wordpad. It should be located in C:users
appdatalocalatiaceprofilesTest.xml
3. You will need to edit some of the values. For me, I set them all to be the same for both GPU's, so that the 2D clock never throttles down. Keep in mind, THE NUMBERS BELOW ARE FOR MY CARD (5970 OC'd). Your values will most likely be different.
Also keep in mind that depending on your card, pc, etc, heat might be an issue depending on what settings you use. In the above example, my card never downclocks even when just using it for just wordprocessing. However, for me heat isnt an issue.
With this fix, the screen flickering went away and has not reappeared after several weeks of using it. Hope this helps.