Before asking what makes a self persist, one can ask whether there is any enduring self to persist. Substance views hold that a single subject underlies a life; reductive and no-self views deny it, treating "the self" as a convenient name for a bundle or stream of impersonal states with no owner behind them.
Answering this shapes but does not settle the persistence question: someone who denies an enduring self still owes an account of why experience hangs together as if it belonged to one person, which the map treats separately under Persistence of the Self.