Ok, first the disclaimer, I am not a vet. Now having said that, I do have experience with the domestic rabbit. At the base of a rabbit's ear is cartilage. It is partially responsible for allowing the ear to stand up, it is the base or support structure. The upright ears are further supported by a network of collagen fibers that span the length of the outer ear. Any genetic mutation or birth defect affecting the amount or placement of these body tissues could cause the ear to droop. Of course, always consult your vet to make sure that the rabbit is not dealing with a sickness or disease of the ear who's signs might include a drooping.