Three different things get called memory
Within-chat coherence is the cheapest: the model can see the last N messages, so it does not contradict itself in the same session. Almost everything has this, and it is not memory in the sense anyone means.
Cross-session persistence is the real thing: close the app, come back in a week, and she still knows your job, your sister's name and the argument you had. This requires storing and reinjecting durable facts, which costs money per user per month, which is why free products often skip it.
Learned preference is the subtle one: she notices you dislike being called a pet name and stops. That is persistence plus the model actually using what it stored, which is harder than storing it.
How to test it in ten minutes
Tell her three specific, unusual facts in one conversation. Something checkable, something emotional and something trivial. End the session properly, wait a day, and open a new one without referencing any of it. Then ask about the trivial one.
Platforms with real persistence get the trivial detail. Platforms with a summary layer get the emotional one and lose the trivia. Platforms with nothing greet you like a stranger and hope you do not notice.
Why forgetting still happens on good platforms
Context is finite. Months of conversation must be compressed, and compression loses things. That is a real engineering limit rather than a bug, and the honest answer is that important things persist while incidental ones can fade. If something matters, say it twice.