I had that problem with my 5d2 while it was still new. Typically, after some inactivity, it would just go into some sleep mode (once or twice daily only), and pressing the shutter would not make it AF. On the other hand, there were all other signs of being "awake". This lasted for a few months and went away.
One possible explanation is that when that camera was new for me, I was pressing the DOF preview button occasionally without realizing it. On the 5D2, it is much easier to do that compared to the other bodies I owned. The camera does not AF then. Now I know how to keep my fingers out of it, maybe this is what solved the problem.