I've seen slo-mo video of a deer completely ducking under a shot that was fired from inside 20yds. This was no slow bow firing the arrow. The shot was where it needed to be. The target moved.
If you're having trouble with this, you need to do one thing:
Shoot at deer that aren't alert.
If you think a few fps (or even several) of arrow speed will trump this phenomenon, you're mistaken.