Second chances aren’t handed out. You earn them with what you do after the first one.

People decide whether to try again with you based on evidence, not on how sorry you seemed. Remorse is the entry requirement and changed behavior is the case, which is why a good apology followed by nothing is worse than none. The period right after a mistake is when everything is being observed. Almost nobody tells you that it is happening.

Pick the specific thing you would need to do differently and do it consistently for longer than the conversation lasted. Do not point it out while you are doing it. Being noticed later is the whole mechanism.