Yes, some Shih Tzus may have dental issues. These can include problems with teeth alignment, problems with gingiva and periodontal disease. Significant dental problems can often lead to your dog refusing to eat or losing appetite. Some of the most common signs of a problem are tooth loss, bad breath, difficulty chewing and shedding excess hair around the mouth. If you notice any of these signs in your Shih Tzu, please consult your veterinarian for help.