Dear [Name],
I am writing to apologize for not keeping the promise I made to you. I know that I said I would [describe the promise], and that I failed to do so. I understand that this has caused you a great deal of frustration, and I want to express my sincerest apologies for not keeping my word.
I want to explain why I was unable to keep my promise. [Describe the reason why you were unable to keep your promise]. I realize that this is no excuse, and that I should have been more responsible in fulfilling my commitment. I understand that I have let you down and I want to make it up to you.
I am truly sorry for not keeping my promise and I hope that you can forgive me. I understand that it may take some time for you to trust me again, but I hope that you will give me the chance to prove that I am reliable and trustworthy. I promise that I will do my best to make sure that this never happens again.
Once again, I apologize for not keeping my promise and I hope that you can find it in your heart to forgive me. I will do whatever it takes to make it up to you.
Sincerely,
[Your Name]