Deer shed their antlers, yet when they die or are killed their antlers never fall off?

I'm willing to bet its some sort of biological process where some hormone/chemical is released that loosens the antler and allows it to fall off. But that process doesn't have a chance to take place if they are shot.

Yep...

Antler growth, hardening, and shedding are regulated by changing testosterone levels in bucks. Changes in day length stimulate the pituitary gland in the brain (via photoperiodism or biological clock) which regulates hormone levels. Falling testosterone levels cause antlers to cleave at their base, and they are shed during late January through early April.

^^^what he said

Most die when they arnt even close to shedding them..

I have found a couple of bucks dead with a shed or sheds right by the bone pile. Found one where I picked up the skull and both antlers were loose.

Ive never personally seen it happen but my grandpa shot a deer where one horn fell of when it hit the ground and another where he pulled the horns off dragging it to the truck. All late season hunts I would guess but don't really know.

That happened to my hunting partner just this last season. He shot an old 10 point and walk up to the buck with only one antler on his head. When he went to pick up the buck by the antler it fell off in his hand and the other side was lying underneath the buck. I didn't believe it until he pulled up to camp with an antlerless buck on his truck rack.