Yes, it's a centerpoint of Kuhn's theory that it's impossible to predict what anomalies, or how many, will lead to a theory's breakdown. Generally, he holds that anomalies will be ignored or explained away, and that only a speculative puzzles are subject to falsification. It's only when the anomalies start becoming really fundamental—like the ultraviolet catastrophe, or the revelation that some crucial piece of instrumentation that produced many of the results the current theory depends on is flawed—that "normal science" ends and "crisis" begins.

This was precisely his argument against the more naive forms of falsificationism.