My own experience was the same with the 5D2 and 7D.... and it happened with almost every lens I own ( which is 9, including four L's ). In both cases, I had focus turn itself off even while attempts were made to focus on good contrasty and well lit subjects. In both cases, rotating the lens in its mount a few times permanently fixed the problem.
I'd have put money on clean lens contacts - they all worked well with my older bodies EOS 350 and EOS 400. Having all the lenses behave the same way... makes me think camera body issues. Having both bodies have the same issue is beyond my thinking.
So, I have to idea what the issue was. Never made an adjustment. After a few partial dismounts - via rotation - the lenses all worked perfectly on either body.
A "go figure" moment for sure.