A. Crowns will only fall off they are not carried out properly. Your dentist probably doesn’t feel confident to carry out the procedure and will not be sure of the success if he did. If it is an NHS dentist he may not get funding for it and this may be part of the reason for his reluctance to carry out the treatment. By the sound of things the tooth which is shorter may have worn down over the years. It happens very slowly so that you almost don’t notice it. It may have happened due to the position of the shorter tooth or the position of the lower tooth that bites against this. If the tooth has worn then the cause of the wear needs to be taken into account before your new crown is made. You may even be able to have a veneer so that the tooth doesn’t have to be shaved down too much. My advice would be to have a consultation with a private dentist who is used to carrying out these procedures. There is no speciality for cosmetic dentistry so you need to ask questions about what kind of training the dentist has and ask whether he/ she has a knowledge of occlusion. Thsi is the study of how teeth bite together. Without this it will be difficult to diagnose the cause of the wear.
I hope this helps
Kind Regards