prevail, persist, die hard, run, endure -- (continue to exist; "These stories die hard"; "The legend of Elvis endures")
persevere, persist, hang in, hang on, hold on -- (be persistent, refuse to stop; "he persisted to call me every night"; "The child persisted and kept asking questions")
persist, remain, stay -- (stay behind; "The smell stayed in the room"; "The hostility remained long after they made up")