Need info on your hardware and ccc version you are using currently. Pls also tell us when it happens, i.e. browsing internet, opening a folder, doing nothing.
I have HD5770. Maybe I had the same problem as you did. The problem happened from CCC 9.10 till CCC 10.4 and it only happened when I was at the desktop, opening a folder or browsing internet, what is called 2D mode. Then CCC 10.5 released. CCC 10.5 was very good for my card. I never had "AMD Radeon family display driver stopped responding" warning message for a month. Now I have CCC 10.6. The problem has started recurring but not as frequently as before. I am curious to know what July CCC drivers will bring.
I remind you, the problem may not lie in the AMD drivers. It may be well due to some other driver in your computer but manifesting itself as a display driver issue.