When I was in the air force I was on a combat pistol and rifle team; and after doing well with that; I came home and totally failed: at being a good shot with a friends muzzleloader.
What I had to do with the muzzleloader was to try and keep the sight on target- until the bullet hit the target.
When I started dropping my arm shooting my bow it clicked in me that I had to do the same thing.
As suggested by the others - keep everything in place until the arrow hits the target.
You might still drop your arm a little- but practicing at keeping in place: will give the arrow time to get too the target.
It really helps accuracy and its a good thing you noticed it.
Don't grasp the bow tight though; maybe others do; but I have found that just letting the handle settle into my palm is best for accuracy. I don't consiously grip the bow at all. In fact I once broke my ring finger on my left hand and had to get a bow sling- to keep the bow from falling to the ground; when I shot. I guess that one finger is holding the bow at the shot?
If you really want to see what sucks about your form; shoot an opposite hand bow. Fred Bear told me this and then laughed at what happened- when I shot a left handed bow. Because whatever you do with the bow you shoot that is poor form: will become horrendously obvious at the shot- horrendously !!!
Being the delight of Freds sense of humor- was humbling enough: to not ever forget!!