Are you using auto focus, or Catch in Focus? If so, the answer is really, really simple. Auto focus sets itself to where your subject is located, the mirror flips up, the shutter opens and closes. The problem is, by the time your shutter opens, your subject is no longer where your camera set focus. I ran into the same problem shooting my own dog a couple months ago. Okay, that sounds bad, but you know what I mean.
You might be able to solve the issue with Live View and continuous focusing - somebody else can comment on that. But I'm a viewfinder kind of guy, especially in bright light. So I dropped back on my old experience-
Manual focus to a spot ahead of your subject, wait until your subject
almost but not quite reaches your pre-focused spot and trip the shutter. The 'not quite' time frame is to accommodate the mirror and shutter lag time.