Have you ever refused to accept someone's apology, or had your own apology rejected?
Yes, once, I apologized to someone, and they didn't say they accepted my apology, merely continued to attack me and call me a terrible person, hated me, wanted to scream in my face, etc.
Not so good. But mostly I apologized so any further attacking would be in the wrong on their part because I had already apologized. It was a sucky situation. I did regret what I had done, but I more used my apology as a defense mechanism.
As far as me not accepting apologies, doesn't really happen. I hate to be in fights with people, even when I'm justified in my anger, I feel guilty for it so I accept apologies pretty much straight away. I can't stay angry. But I hate when people don't actually apologize they say something like "I'm sorry you're hurt" or "I'm sorry you feel that way" because then they belittle you and actually act like they haven't done anything wrong. One person I know, never apologizes at all, he just tries to comfort me for being hurt or tries to fix the rift, without admitting he was wrong. It drives me crazy.
All I want to hear is "It was wrong, I shouldn't have done/said that, and I'm sorry."