When they ask for forgiveness, what do you say? Of course, you'll forgive. Because the worst thing you can do is NOT to forgive. As Giles said in the "I Only Have Eyes for You" episode of "Buffy the Vampire Slayer": "To forgive is an act of compassion, Buffy. It's not done because people deserve it, it's done because they need it."
Put yourself in their place. Imagine asking for forgiveness from someone for your own peace of mind, and not getting it. Forgiving one's self is difficult enough. There's no need for you to make it harder.
Now, when the person still offers no apologies about what they did, when they act as if they did nothing wrong and continue treating you as if you're making a big fuss out of nothing, then that's different. Waaaay different. Because you don't want to be the same idiot who get burned again big time by the same person. As the saying goes, "fool me once, shame on you. Fool me twice, shame on me."
What's more, I'm not averse to giving people from my past a chance to be in my present life. Some people ARE worth having and keeping in your life. It simply takes awhile to figure out what their roles are. You can give them the same role as before. Or maybe, just maybe, they're due either for a promotion or demotion. It's your call.