Mine does the same thing. He does not always eat everyday. Shih tzus are very picky dogs. Avoid feeding them table scraps and that should help. He could go several days without food, but he will eventually eat. Dogs will not starve themselves to death. Try adding a little bit of canned dog meat (like Caesars for small dogs) or add a little bit of low fat, plain yogurt (unless he's allergic to dairy). Shih tzus are also smaller and so their energy runs out more quickly. If he's not eating, then he's not having enough calories and so he'll sleep more also. Puppies also sleep more then adults too.
