If your Shih Tzu is refusing to eat their food (and it's something new that you haven't seen them eat before), you probably have a picky eater on your hands. Dogs that are picky eaters will outright refuse to eat the food that's been given to them, especially when they know it isn't their usual food. If the food isn't new, you should know that a lot of various health conditions and illnesses can cause decreased appetite in a small breed of dog. Try switching back to your dog's original pet food before seeking veterinary advice.