Personally, I sit way more than I stand and I never hold my bow in my hand. I always position my bow hanger so that it is in the optimal position to just reach out and grab it. Being right handed, it is usually on my left side.

Maybe I've just been lucky, but I've never missed a chance because I was sitting down and my bow wasn't in my hand. Even while snoozing, I have a weird sort of 6th sense where I somehow detect an approaching deer whether I hear it or just think I heard it.