Since you're a marksman you should probably already know this, but just remember bras when you shoot. Breath, Relax, Aim, Squeeze- take a breath in and let it 80% out then hold and relax. That should steady you up a little bit. Also, being strong at somethings isn't necessarily strong at others, just practice holding steady, do some shoulder exercises, develop muscle memory like Dwight said. A lot of things can affect your stability, I wouldn't give up on it, just look for what works.
Just doing the best I can.