I would imagine the excitement of hunting is enough to keep target panic at bay, at least for now. Target panic isn't a constant thing, it keeps changing.
Your description of being able to close your eyes and hold the bow at anchor forever, but when you open your eyes and see the spot, the arrow is gone, makes me think you are a good candidate for a trigger, because that's exactly what a trigger does: you hold on the target until the trigger goes off, and the instant the trigger goes off, the arrow is gone. You're doing the same thing by closing your eyes and then shooting as soon as you open them, but of course that isn't a particularly effective trigger, since you aren't aiming at anything when your eyes are closed.
Popular triggers are clickers, touching a feather to your nose, or home-made gadgets you can snap with your thumbnail. Anything that is sort of under your control, but where you can't guess the exact moment it will go off.