Then they're still mad at you and you have to accept that.

[Said kindly, but very firmly.]

Apologizing doesn't mean they have to forgive you or stop being mad. They don't even have to accept the apology. Apologizing isn't for your sake. It's for theirs. To let them know that you are sincerely sorry for having hurt them in some way. I know that it hurts to not be forgiven and to have people mad at you, but you can't control the actions or feelings of other people.