Hi Smudge..I am not sure how to answer this question. But, my first thought is forgive yourself. You have apologized and asked for forgiveness and they will not give it to you, doesn't mean you don't deserve to be forgiven. Also, who are you asking?
If you are asking a partner who is abusive towards you? Then they are probably refusing to forgive you as a form of punishment for whatever it was that you may have done.
I guess more information is needed for me to understand this. If the person you are asking is someone who is genuine and who cares about you? Then I would think they would forgive you without you even having to ask.
So, sorry if that doesn't help. But I suspect the person you are seeking forgiveness from and they are refusing is perhaps not someone you need in your life right now??? I don't know. If it is someone who is abusing you..they are not forgiving you on purpose to hurt you back, or to punish you, or to manipulate you in some way.
Focus on you and forgive yourself. We all make mistakes, we all deserve forgiveness. Perhaps more details would help me to help you better?
Smudge, another thought I had. If you truly hurt someone and they are not forgiving you, despite your asking, maybe they are not ready to forgive you? Maybe they are so hurt that they are not at the point of forgiving you? And, maybe, if you really did hurt them, then maybe do right by giving them the space and time they need to heal. We have all been hurt and hurt others in our lifetime and we can never really know how someone else is feeling and at what level their hurt is. You may have hurt by throwing a "pebble"..and they may feel like they were hit by a "two ton boulder".
If you truly care about this person, give them the time and space they need. They probably don't trust you not to hurt them again. Very natural for someone who has suffered a deep hurt to react.
On this forum, when we suspect someone is being abused, or has been abused, we suggest and encourage 'NO CONTACT". That person you hurt may be feeling THAT deep kind of hurt and will not respond to you as they know if they do, it could open up another opportunity to be hurt by you again.
Perhaps, respect this person and let them be. They may just not be ready to forgive. Take care of you at this point, you may or may not have made a mistake, forgive yourself and try and go forward.
I don't know in what context you are asking this. I hope my answers help in someway.