Famous for taking their time
It helps to start with the truth: Shih Tzu puppies are widely considered one of the more difficult breeds to housetrain, and owners who know that in advance do far better than owners expecting a fortnight's work. Nothing is wrong with the puppy's intelligence. A Shih Tzu was bred for centuries as an indoor palace companion, a dog whose world was carpeted rooms and laps, and that heritage produced a small dog who is comfortable living inside, particular about weather, and not naturally inclined to ask clearly to go out. Housetraining a Shih Tzu is a project of months of consistency, and it succeeds through management far more than through any clever technique.
The specific hurdles with this breed
Size comes first: a Shih Tzu puppy's bladder is tiny, control develops slowly, and the gap between needing to go and going can be seconds. Surface preference comes next, and it is the breed's signature problem: puppies raised on soft flooring often read rugs, carpets, bath mats, and bedding as appropriate places to squat, because to a small puppy they feel like the pads and papers of early life. Add a low tolerance for cold, rain, and wet grass dragging on a long coat and belly, plus a talent for going quietly in another room while you assume she is asleep, and you have a puppy who can appear trained in the kitchen while maintaining a private arrangement in the spare bedroom. Weak signalling completes the picture; many Shih Tzus drift to the door and wait in silence, once, briefly.
Management that actually moves a Shih Tzu forward
Shrink the world and raise the trip count. Your puppy lives in the room you are in, behind a gate, or in a pen on a hard, cleanable floor, and she earns new rooms one at a time, only after weeks without accidents in the current territory. Take her out far more often than feels reasonable: on waking, after eating, after drinking, after play, after a chew session, and at short set intervals between those anchors. Always use the same door and the same small patch, wait her out fully, and praise her warmly outdoors the moment she finishes, because the Shih Tzu responds to delighted approval and tasty rewards far better than to any sign of your disappointment. Lift or gate off rugs during the training months and treat every carpeted room as advanced territory. Keep a written note of accident times for the first weeks, since this breed's pattern, often a particular hour and a particular room, is the single most useful thing you can learn, and it tells you exactly where to add a trip and a barrier.
When slow becomes a question for the vet
Judge a Shih Tzu by the trend over a month, not by the week, and expect the full job to take longer than it did for your neighbour's retriever. Still, some patterns deserve a veterinarian's input: a puppy who strains, who produces constant tiny puddles, who drinks noticeably more than expected, or who suddenly loses ground she had firmly gained. Those are health questions wearing a training costume. Resist comparing and resist giving up, because Shih Tzus trained with patient management do become reliable, and spreading the many daily outings across the household in KinsLe with Care Teams, each trip timestamped once completed, keeps the volume of repetitions from exhausting one determined person.