You can only apologize so much for any hurt, or offense you've caused someone in the past. If they can't or won't forgive and see that you've changed, and that your remorse is truly sincere and your apology from your heart, then you have no other option but to let them go and to continue on without them in your life. That doesn't mean you give up on them, but it means you need to give the matter over to the Lord and trust He will work to mend the broken bond between you.
God has called us to peace, and Jesus said that peacemakers are blessed. It's unfortunate some would rather cause division and hold on to their anger. Rather than heal or let someone else heal, they choose to harbor resentment and wear it like a medal to solicit pity and attention. You cannot change another's heart, you can only offer an olive branch . . .they must reach out and take it.
Please Forgive and Forget ~ God does! He also says those who do not forgive cannot be forgiven by Him . . . sober warning!
In His Love,