Shooting at a deer that knows something is up is a bad deal.
That being said, they don't actually SEE the arrow coming and try to dodge it. A deer's natural reaction to a noise or movement that startles them is to bunch-up and dart away. No matter how quiet your bow is, they will react to the sound and movment of a shot. When they do that, it drops their body position. Just like a person who can't leap from harm without bending the knees, when a deer gathers itself to flee, it bends all four legs for a jump.
If they think something is hinky and have a spot to pin it on, they are preprogramed to react away from that location.
Close your eyes for a cout of 100, slow your breathing down and wait it out. Slowly open your eyes and see what's up. If the deer is still on alert, go through the process again. Just relax.
Too often I have hunted with friends and watched this whole thing play out. Even when the deer eases up and calms down, they either make a hurried, jerky attempt at a draw or they try the sneaky inch by inch thing. Both result in a bad, tension laden attempt at a shot.
If the deer calms down enough and presents a good shot, be just as smooth as if it never knew you were there.
Deer are ALWAYS on alert to some degree. Eons of being on the tasty end of the food chain has ensured that all the laid-back deer were eaten centuries ago. But a deer that has its radar tuned specifically in to you is a difficult target. I would wait it out and see what happens.
OkKeith