This is an issue that Riot has known about for over 2 months now and has done nothing to fix. It started with complaints from NVidia users, and then the complaints from ATI users started pouring in. I use an AMD HD 7850, and I have the same problem at random. Game will freeze, go black screen, and after 10 - 15 seconds it will come back.
Here is the thread on the Riot forums.
Any help from ATI would be greatly appreciated.