Many big game animals will jump the string -- that is, react to the sound of your bow going off. When you release the string, the animal actually bends its legs and drops down before leaping forward, and that's about the time your arrow reaches the animal. So you end up shooting over the animal's back. Skittish whitetails are particularly notorious for jumping the string.
As you're getting ready for the shot, try to get a read on the animal. If it looks nervous, you can bet it will drop to run when it hears the shot. A deer can move an amazing distance between the time it hears the bow and the time the arrow arrives at the animal's position. The distance the deer moves before the arrow arrives obviously depends on the animal's response time, but it also depends on arrow speed and shot distance. Of the three, the quickness of the deer and the range are the biggest factors. If you aren't sure how the deer in your area react to the sounds of bows, ask someone who has hunted there. If they've shot at many deer, they will know.
Here's a good rule of thumb: If an animal appears nervous, always aim a little low, but don't aim too low. Aim right at the bottom of the vitals, three or four inches above the brisket. That way, even if the animal doesn't drop you'll still make a killing shot.