Ok guys, I just tested out my 7D with my 70-200 f2.8 (previously only been using 135 f2) and this issue seems AI Servo specific. SLK Photo, did you notice this too or does your issue occur in one shot? It seems like a body problem, not a lens problem. Mine occurs in AI Servo only though, one shot and live view AF is spot on. I've tried everything - use one AF point, use certain AF points, use more AF points, changed settings.
I know my 7D well enough (been with it for almost 3 years), and having used older Canon EOS digital models, to know that this behavior isn't normal and that this isn't a settings issue (at least on the surface). And I've already done a 'reboot' by taking out the main and watch batteries, and the issue still occurs.
A lot of folks seem to blame the AF points but my experience shooting runways for a couple of years and then switching to sports (both dealing with moving subjects) is that Canon's SLRs from the DIGIC 1 and DIGIC 2 days have already been intelligent enough to not be easily fooled (although it can happen, but very occasionally versus every other shot in this situation) by nearby objects and such.
Even when subjects have moved off the area covered by AF point(s), there's always been a split second allowance 'lag' that focus remains intact for the 0.5-1 second a subject moves off from AF points (seems the logic behind this is in case the subject comes back in), before the camera decides "ok the subject isn't coming back, readjusting focus).
It's safe to assume that something that you can't repair yourself has gone wrong and you should send in your 5D3 for a checkup (that's what I'm going to do with my 7D)
I'm going to contact Canon on Monday to arrange for my 7D to be sent in. However I haven't dealt with Canon USA service before. Do I call or email them explaining my situation? Do I have to pay for shipping there and/or back? How long does service typically take?