No one can answer what another human being will accept. If that person is one who trusts words and actions of others, if they have the capacity for forgiveness, if they feel your relationship is worth salvaging, then sure they will make the effort to repair the broken part of your relationship. But, if they feel they have been hurt beyond their limit, or they do not have a capacity for forgiveness, etc....then I would say that the relationship cannot be repaired. That being said, it doesn't mean you shouldn't take responsibility for your actions and put your heartfelt apology in words and actions out there for the other individual to do with as they see fit. You will feel better for having done that and you will know that you truly tried to repair the damage. From there, it's up to the other individual.

Good luck to you, and I pray your relationship can be healed.