If you look at the haircount charts from the study, propecia doesn't just suddenly stop working, but the haircounts, after initially rising in the first two years, tend to very gradually diminish, but the average count was still well above the baseline, even after five years. Propecia isn't a cure, and even if you're an excellent responder, you'll probably eventually lose hair on it. But if it works for you, it will probably buy you a lot of time before you noticeably degrade from where you are at the peak of your results.
It never stops inhibiting DHT, but for whatever reason, the effectiveness can wear out. There are a great number of theories as to why this happens.