Many things persist, and that includes human memory. But in order to understand persistence conditions, we should make a conceptual distinction between personal and impersonal identity. The persistence conditions for something impersonal (X) are different for something/someone personal (call the personal entity, S).
Kevin Corcoran illustrates persistence conditions for X by using the example of a banana. X, in this case, may be green at one time, yellow at another, and brown or black at yet another. However, X is still the same banana or the same X in each case. What permits me to make such an assertion?
Rene Descartes gives an example of wax in his work Meditations. Even if we melt the wax (X), something remains that lets us know it's the same parcel of matter, even if melted wax does not have the same properties as non-melted wax. What are the persistence conditions for bananas and for wax?
However we answer that question, Corcoran reasons that persistence conditions for persons (S) apparently exist too. Some suggestions for what makes a person (S) the same at T1, T2 . . . Tn are the soul theory, memory theory, the body theory, and the illusion theory. All of these discussions are framed within the context of Leibniz's absolute identity theory. There is no unanimous answer on the persistence conditions for X or S.