Benchmark test crashes to desktop.

I have an AMD HD6700 (2GB) video card using the newest (beta) driver from ATI that was specifically made for DA:I and FarCry 4. At times I can play the game in Ultra mode (I have a 3.2 GHz Quad and 16GB of DDR3 RAM) and it shows off the game beautifully. Then, the stuttering starts after about five minutes of gameplay. I have reduced the specs to minimum and the graphics change somewhat, but the stuttering remains in the cutscenes and in combat after about five minutes. What can I do to prevent the sound stuttering and the framerate dropping?