kaihp, thanks for the update and I'm sorry to hear about your latest experience. The AF in the 5D3/1D X is quite tricky to get the hang of, and the first many times I used it, I had the same experiences. Until the 7D, I never bothered with anything other than center point AF, and with the 7D, Zone AF was good, but not great with AI Servo. My first experiences with the 5DIII were with birds in flight and it would always focus on the sky, and not the bird. I came to realize that the AF points are bigger than they seem and I was focusing on the bird when it was too small in the frame. I also realized that I wasn't waiting for the confirmation light.
In your situation, it's hard to know exactly what might be happening, but here's a brief list of some of the things I've run into with the 5DIII and AI Servo:
1. Not waiting for AF confirmation
(as I said above) - this requires a split second of patience, but feels like forever in the heat of the moment.
2. Focusing on too small an object
(as above as well) - the AF sensors need a reasonably big area to focus on for the initial AF lock
3. Moving the lens too much during AI Servo lock
- that makes it easy for the camera to lose the lock. Smooth pans/movements work best
4. Selecting a non-cross point as the initial AF point
- there's a way to make the AF points blink so you know which are cross, and which are not, make sure this is turned on...
5. Fussing with the AF settings too much
- the standard settings work well, as soon as you start adjusting the values + or -, things seems to go sideways
6. Not having my lenses microadjusted
- with the 300 f/2.8, I went out the day I got it and was dismayed that all of my photos are slight out of focus. After FoCal and a +5 on the lens, the photos were all sharp
7. Bumping the diopter adjustment
- this is the most annoying issue because it's so easy to do, but only happens often enough for me to forget that it can happen. I put the camera to my eye, see the AF lock but the stupid frame looks blurry??? After trying a few more shots, I realize what I've done!
8. Shooting in the dark
- okay, not really, but unless you use the center point as the initial AF point when the light is pretty low (e.g. ISO6400+, 1/100s, f/2.8 with the 300mm) you won't get too far.
9. Having AF tied to the shutter
- this is the rarest one for me because I use back button AF almost all of the time, but when I allow the shutter button to control AF and then forget I've set it to do that, that always throws me off for a moment.
and particularly with the 300 f/2.8:
10. Depth of field
- 300mm at f/2.8 is sometimes too shallow to get everything in focus, which also means that if you don't nail focus, your photos will be blurry. I will often choose to shoot at f/2.8 to blur out the background, but I know the trade off will be that roughly 50% of my photos might be out of focus in some situations. Shooting at f/4 is much safer, but may not be practical if the background is a mess.
I'm not sure if any of these might apply, but hopefully you and others can learn from my many mistakes