izumirati

1. (of species, peoples, villages) to die out; to be dying out
   Mnoga sela na jugu Srbije polako izumiru. — Many villages in southern Serbia are slowly dying out.
   Ova vrsta ptica izumire zbog zagađenja. — This bird species is dying out because of pollution.
2. (of customs, crafts) to disappear; to be dying out
   Stari zanati kod nas izumiru. — Old crafts are dying out here.

The perfective is izumreti; izumrla vrsta means "an extinct species".