Certainly short teeth can have a crown, but the retention (the ability of the crown to stay cemented onto the underlying tooth) is greatly influenced by the size and length of the tooth above the gum line.Alternatives include having orthodontics to extrude the tooth, giving more tooth structure above the gum line.Or, crown lengthening, meaning removing some gum and bone around the tooth. This is often a great way to treat back teeth that are short, but front teeth may end up looking too long and possibly esthetically objectionable.In some cases dentists must resort to doing a root canal on the tooth, then placing a post and core to build up some "tooth structure" for the crown to stay adhered to.As a last resort, as happens many times when a tooth breaks off at the gum line, is to get an extraction and dental implant or possibly a bridge.If your crown keeps coming off I'm sure your dentist is as concerned as you are and can recommend the appropriate procedure to enable him/her to make a much more retentive crown for you.Good luck!