The Root of the Behavior
You may notice that Daphne has gunk in her eyes quite frequently, which can build up and lay on the hair that surrounds her face. Secondly, Shih Tzus can have diseases that cause their eyes to tear, which will also contribute to the build-up. If the hair around your dog's eyes stays wet, bacteria can also build up and it may begin to smell. Sometimes, people will think the smell is from bad breath, but it is actually from the eyes. Your dog can have bad breath, but that is only common if you do not provide your dog with the proper grooming care. Beyond these health concerns, you may want to check out your dog's anal glands. If your dog smells profusely, they may have backed up anal glands that need releasing. There will be a gland on each side of your dog's anus and they can fill up with liquid easily. If these health concerns do not seem common in your dog, you may want to get your dog checked out with the veterinarian.
Encouraging the Behavior
Secondly, if you notice that your dog has gunk around their eyes, you may want to see if your dog has allergies or if it is allergy season. Allergies can enhance eye issues within your dog and they can also provoke negative smells. Although health issues may be a concern, you may just need to bathe your dog more often. Sometimes Shih Tzus have oilier coats because they have longer hair. If you can bathe your dog every week or two, it may make a world of difference for her and for you.