persisti

Persisti covers both halves of the English word. A person persistas when they keep at something after the point where most people would stop; a condition persistas when it simply refuses to go away, which is how you get la doloro persistis and la kutimo persistas. The first is a virtue and the second is usually a nuisance, and Esperanto is happy to let one verb carry both.

Watch the seam that is not there. Per is a real Esperanto preposition, meaning by means of, and the temptation is to read persisti as per plus a root sist-. There is no such root: persist- came in whole from Latin, where the build genuinely was per- plus sistere, to stand. Esperanto borrowed the finished word, not the recipe. The same warning covers insisti and rezisti, which sit in the same Latin family and are likewise single roots here.

Where it differs from the neighbours is worth a line. Daŭri is neutral duration, a thing simply going on. Persisti adds resistance to something: the weather persists in spite of the forecast, the learner persists in spite of the grammar. Insisti is about saying so out loud, pressing a demand. And obstina is the character trait, admirable or infuriating depending on who is describing whom.