I don't shoot a lot of sports, but I would guess that your choice of lens is most of the problem. Lenses focus at their widest aperture, which means you have a very thin depth of field upon which to lock focus. With moving target, the tiniest of movements will make shots drift away from sharp focus. I know my 85 f/1.2 is VERY finicky and slow about locking focus. That handicap, combined with your low f-stop means you had potentially missed focus lock and a razor thin margin of error once you fired the shot. In your situation, I would have lowered the shutter speed in favor of a higher f-stop. That would give you a little more latitude when the focus wasn't spot on. You also have a ton of choices for AI Servo on the 1DX and you may not have been using the ideal settings for that type of action. I have shot some indoor tennis matches with my 1DX and a 70-200 f/2.8II -- I would imagine that to be even dimmer than your gym (miserable light to play in much less shoot). I was able to keep 1/250 and about f4 for most of the shots. The racquets and balls were frozen, but there was little motion blur with the people. Granted, I only had a single moving subject to lock onto, but the focus tracking stayed spot on. Since I was shooting tennis, I used the AF mode with the little tennis icon and kept it's default settings.
1/250th is not going to work. I won't shoot slower than 1/500th with a 135mm lens. I cannot have motion blur for the type of photography I am shooting.
I think most posters are misunderstanding the problem here, but I thank you for your detailed response because they are valid considerations. The poster helpful is getting what I am saying.
The real issue is the "worse" EV tolerance for AF on the 1DX in high fps vs. less fps or one shot. It makes no sense to argue that it's DOF when 1. In well-lit gyms, I don't have this problem. I have shot hundreds of in-focus photos in a row with the 135L at f/2. 2. I lock focus on shot 1, and it randomly goes in and out of focus throughout the shot burst, annoyingly. For instance, shots 1, 2, 3, 8 are in focus, while shots 4, 5, 6, 7, aren't. This is clearly a low light AF issue with the lens/camera combination and not DOF.
Why would I say that? In enough light, this never happens. In Ashland's gym I shot over 450 photos, all in high burst mode for instance, with the 135L at f/2 and not one was OOF. I have gathered some inside info since my first post that the 1DX in high burst mode is sensitive about -0.5EV whereas about 10 fps and much less it gets better, to -1EV to -2EV. This is the issue I was looking for.
Again, thank you for all who posted or messaged me. I appreciate the help.