I hate to sound negative but sometimes, going back to friendships like that is like going back to jail - if it happens, there's probably a not-very-pleasant reason why. Without going into too much detail, I had a similar situation about a year ago, caused over a misunderstanding about something when I had a meltdown (and it wasn't like said person, who is NT, hadn't had meltdowns of her own - some while sober, most not.) I apologized, made it clear that I was open to reconciliation, and hear from common acquaintances that she's still on about what happened.
Some people want reconciliation. Some people find more comfort in anger and rage than they do forgiveness. If this person isn't willing to grow up, as painful as it seems, maybe it's best not to have her in your life, especially if it's going to go back to the dysfunctional way it was before.