Antler dropping is controlled by the same thing antler growth is......testosterone. In wild deer, this level is determined by amount and angle of daylight as well as health of the animal. Injury to the testicles of a deer may not only inhibit growth of antlers, but inhibit the dropping of said antlers. Same is true for the pedicle. High populations of large bucks in an area means more sparring for a longer time, which can keep testosterone levels high enough that bucks hold the antlers longer. Those increase in sparring also means more chances of injury to the testicles or pedicle. Also means more chance of a broken antler. Around here, how healthy a buck goes into winter along with how hard the winter is, has a big affect on when they drop their antlers. Still, the drop in testosterone effects both pedicles the same, so a difference of two months in the dropping of individual antlers, tells me something is amiss. Hard in the OP's pic for me to determine if there is a stub of antler left or just an empty pedicle, even when downloaded and enlarged greatly. Be interesting to see what that buck grows next year.