how to win someone back?

I made a mistake and I acknowledge the fact that I did.

I know I have to make up for it and improve in any way that I can - not just for myself but for the both of us. Even though I know and feel that things improved already - but I know how much he was hurt about it.

and now I’m getting tired of chasing.. making up.. apologizing. i know that it is rude of me because I am in the wrong here. it’ll take long enough to gain even the slightest bit the thing I lost.

but for his peace of mind.. his security.. his time.. should I just agree to let him go? am I making things worse? am I just holding on the thought of “us”?