It is normal for some "eye gunk" to seep occasionally from a Tzu's eyes...and some dogs will have health issues that cause the eyes to tear quite excessively. Both of these issues can cause Shih Tzu odor. What is actually in this stuff? Both tears and so-called gunk will contain water, sweat, oils, saline, mucus and small amounts of a fatty tissue called meibum. Put this all together and allow it to sit on the hairs of the face and it will begin to smell.
It will also cause tear staining most of the time. Not only do the substances alone have an odor, but if the hairs on the dog are wet most of the time from this, bacteria can begin to grow (this is what tear staining basically is) and even without the classic discoloration of hairs, the dog can have a bad odor.
Some may mistake this for bad breath, when in fact the smell is coming from under and around the eyes. The most important step that you can take is to ensure that this area stays dry. If excessive tearing is present, it is time for a check up with the veterinarian. If allergies are the cause, many steps can be taken to help your dog.
It will help to wipe down this area each morning when it may be at its worst. This can be done with a hypo-allergenic canine facial wipe or a scent-free baby wipe and then a dry, soft washcloth. Inspection should be done several times during the day as well. It only takes just a moment to clean around the eyes.