I gave him an apology letter, but he has not replied – now what?

Loving someone is not enough. You have broken off with this man several times. Really look at that and understand that love is not enough. Take inventory – yours and his – where were the failures. You might not be good as a couple and fully understand one another.

Additing on to my post,being friends and hanging on will likely only hurt you in the long run. Best to move on and if the universe means you find your way back to each other, so be it.

Have you changed for real? Because from an outsiders look you are doing the exact same thing you have done before: rekindle. Maybe the last break up was worse than what happened before but still: whats new?
I also agree with paige that if you really want to aplogize give him space in how he goes about it. You kept right on with asking for a lunch date. Pace. In all honesty i dont believe in third and fourth changes. Its a sign something always will be off. Maybe its time for you to move on

Thanks everyone for the responses, although some are difficult to read. But this is a difficult situation. I do think that he has every right to not reply. And I have changed, in response to that question. I definitely am not using work avenues to reach out to him (email, phone) and I have done a really good job at giving him space and only saying hello if I do happen to see him (I am not seeking him out). I knew breaking it off was a mistake when it happened and, I hate to admit it, I am a romantic at heart and I believe in fate and I will always have hope. That said, I don’t plan to try any additional contact and I’ve made my peace with this being maybe the last contact I’ve had with him, despite how much it hurts. I have even altered my work schedule a bit so I won’t be in my office when he needs to be. I owed him the apology and I went through several variations of it before I got it exactly like it should be—accepting blame and telling him it was long overdue. (To clarify further, we were friends first and the reason I offered friendship was to extend that option and let him know that I don’t want to fast track anything, if he is interested in being in contact at all. As far as offering lunch, it was an offer within the letter and he can accept or decline. I don’t feel that’s pushy.)

Update: I wanted to come back and post that I did have a meaningful talk with my ex and we even had some humorous moments. Afterward, it was like a weight had been lifted and it felt so right to have talked like we did. He initiated contact and he said that he is still healing and it’s too soon for lunch, but that he hopes we can take baby steps in that direction and rebuild a friendship. I am posting this for anyone that has hope and believes in fate like I do. But I also want to add that I gave him the apology letter and then left him alone to his thoughts, despite how hard it was (especially during the first 24 hours) to get out of my head and realize that I may never talk to him again and that I OWED him the apology. I fully intend to respect his boundaries and let him reach out to me and gradually build trust again, over time (because this is a lesson learned). Good luck to anyone that stumbles upon this post in hopes of figuring out how to regain your ex’s trust or just reaching them again. It is a delicate and sometimes difficult feat, but it can be done with respect, and after personal growth.