Self is a function that changes over time but in being self referential, the changes include the previous states of itself at least "grossly". So it's like many natural processes. The sun is the sun but the sun is always changing. A hurricane is a hurricane, etc. The difference being that self is an active perspective. Still groggy from waking. Certain brain damage can make self less apparently persistent, screwing up the self-referential thing. Though from an alternative perspective (someone else observing you) it may seem even more persistent.