I'd say a more accurate analogy would be something like this:
You break the trust of a loved one. You want them to think of you the same way they did before you lost their trust. Waiting around and hoping that they'll simply forgive and forget doesn't make much progress, and if you continue to give them reasons to suspect you, even if they don't actually catch you doing something wrong, you're harming your redemption in their eyes. The only real way to repair their trust in you is to actively present yourself as an improved individual.
Your Honor level represents Riot's trust and confidence in you. Getting multiple chat restrictions in a short span of time, or committing a flagrant and serious offense against the Summoner's Code, will drop you down to Honor 0, indicating that Riot has no real faith in you as positive influence in the community. You can't change that opinion simply by sitting around for a long period of time, and if you're actively giving them reasons to see you as a negative influence, you can't expect your honor level to recover.