Why does my parent tell the same story over and over?

Usually because they're working on them.

Robert Butler, the gerontologist who gave us the word ageism, put a name to this in 1963: the life review. His argument was that going back over a long life is not idleness and not decay, but a task late life sets: a person sorting through what happened and deciding what it amounted to. The telling is how the deciding gets done.

Which puts the fourth telling in a different light. You aren't watching a fault. You're watching someone do a piece of work out loud, in the only place available to do it, which is in front of you. A story that keeps coming back is generally one that hasn't settled, and each pass is another go at it.

By the shape of it, and not by yourself.

Life review has a story in it. A beginning, people with names, a point being made, holding together the same way each time even when the emphasis shifts. Your parent knows they've told you before, or is untroubled to hear it. What tends to look different is repetition inside a single conversation, a question asked again a few minutes after it was answered, or an account that arrives with no frame around it and thins out rather than deepening.

That is a description, not a test, and it's a reason to raise the subject with someone qualified rather than a way to settle it from the sofa. Ordinary aging, medication effects, depression, hearing loss and early dementia overlap here, which is precisely why the assessment is a clinical one. If the question is live for you, it goes to their physician.

Ask it something new.

The instinct is to show you've heard it, which reads as we've done this however kindly you manage it, and closes the thing down. The alternative is free: put a question to the story you've never put to it. What their mother said about it. Whether anyone tried to talk them out of it. What they thought was going to happen next.

There's something worth listening for while you do. The beat your parent keeps returning to, the detail that carries the weight every time, is usually the part that hasn't resolved. That's the corner to ask about. You're not being humored into an old story again; you're being handed the piece of it that still has a question in it.

Related: How to have a real conversation with your aging parent walks a visit through start to finish, and Talking to the People Who Taught You to Talk is the longer argument.