You may have a setting in your camera called something like “Release Priority”.
If so, your choices will be “Shutter” or “AF (focus)”.
If it is set to “Shutter”, the camera will shoot regardless if the subject is in focus or not.
If it is set to “AF”, the camera will not shoot until it has a precise focus lock.
You may think it is in focus, but the camera doesn’t. So in “AF” mode under “Release Priority”, it may just be hunting for focus on a moving subject.
Low light situations are also a problem. Look for another setting called something like “AF assist beam”. That should be turned on. The camera will send out an infra-red beam that lands on the subject. It has a pattern on it that the camera can see and helps it focus easier. You will not see this beam unless it is very dark. It shuts off just before the photo is taken.
Point and Shoot cameras also have a notoriously long “Shutter Lag”. Sometimes taking the photo ½ second after you actually press the button. There is nothing that can be done about this except for upgrading to another camera. Look in the specs for “Shutter Lag” timing specifications before buying a new camera.
Most specs and comparisons can be found at DPReview