BEFORE you send it in for repair...
You said it sometimes does this at "events". Can you please describe the shooting conditions at these events? Would you characterize them as having low light?
I ask because there are a variety of reasons why a perfectly good camera can fail to focus or shoot. I'll explain.
The "default" shooting mode on a 60D is "One Shot" mode. But what you might not necessarily know is that this mode is ALSO Canon's "focus priority" mode. THAT means that if the camera fails to lock auto-focus on the subject then the camera WILL NOT SHOOT (and that's on purpose... it's programmed to do this.)
You can also switch the camera to "AI Servo" mode. That mode is really designed for sports (and you should not use it unless your subject is moving or you can get focus errors), but that mode also switches the camera to "release priority" mode. THAT means that the camera WILL take the shot when you fully press the shutter button whether it was able to lock focus or not.
You can also switch off AF on the lens.
Other reasons why cameras sometimes don't fire is if you've switched on a self-timer mode -- although you'd probably figure that out when the camera fires between 2 or 10 seconds later and powering the camera off and back on wouldn't clear the behavior.
But I have seen cameras where turning it off and on only seems to clear the behavior because in reality the camera just happened to catch some contrast somewhere and was able to lock focus.
Remember that the AF point is looking for contrast. If the AF target points are on spots that have almost no contrast then the camera can fail to focus... especially if it's dark.
Yes, I have it primarily set to one shot focus as many of my events are low light, and I found focus to seem to work better on that setting. I do try to pull back and re-focus with high contrasting elements before I turn it off and on, but it still won't work without turning it off sometimes. I tried switching to al servo but noticed the camera had a harder time focusing in the light I was working in, so went back to one shot. Froze on me 3 times. If it makes a difference, I noticed it only with my flash on. If I switched the flash off and worked with available light it was ok---but cant recall if that's been the case in the past.
And as for switching manual focus, I really think my sight is not great enough. I wear glasses and everything, but have tried focusing manually and then switching to AF to see if I'm on point. I'm always a bit off.