It depends, what line did they cross? You can forgive them and not subject yourself to their treachery again. Is this something they continue to do and therefore are untrustworthy? Are they a gossip, for example, and therefore you cannot confide in them? You can reconcile but set up boundaries such as not sharing private matters with them.
If they shamed you in front of the whole school with some horrible joke, and you actually managed to forgive them and still wanted to be friends with them, how do you suppose that would make them feel?
Doesn’t scripture say we love much because we’ve been forgiven much? How true could that be in a friendship, that has been tested and yet sustained? Not to say you should go out of your way to test your friendships by doing horrible things, but if someone makes a mistake or does something in poor judgement, will you hold their sin against them when God has forgiven you of all of your sins? Imagine when they see that you are a faithful friend, who accepts their shortcomings.
Careful that your lack of reconciliation isn’t in a lack of forgiveness or in bitterness. You may justifiably be hurt by their actions, but if they are trying to make amends, why do you stop them from doing what God has commanded them to do? To right their wrongs.
Considering the severity of the offense, it isn’t necessarily required for you to continue the friendship if it’s just not a healthy friendship, such that they are always putting you in temptation’s way or are acting as a bad influence in your life. What fellowship does light have with darkness?
You may have to “hand them over to Satan” as scripture says for those continually in sin. What this means, is that they get to experience their sin with a lack of fellowship from you. “While I forgive you, you need to deal with that problem that keeps coming up, and until you do, we will have to part ways.” You are under no obligation to subject yourself to their wrongs, that they may have no intention of changing.
Proverbs 17:9 King James Version
9 He that covereth a transgression seeketh love; but he that repeateth a matter separateth very friends.
I think you should make your decision wisely and consider love. It keeps no record of wrongs. Forgiveness is a given, full on reconciliation and being welcomed back into your life should be weighed. Your aim should be reconciliation, that would be nice wouldn’t it? To see past their wrong, they repent, and you have a wonderful faithful friendship. Removing them from your life should be a last resort.