Hi bokenentity, sometimes things won't go back the way they were before but after time, healing, building back up the trust and learning from mistakes depending on the situation some relationships can grow even stronger.
Sometimes it can take months/years for trust to come back if it does so I suppose it depends on the nature of the relationship and what it means to you. Perhaps try talking to the person about how they really feel about the situation (without putting any pressure on them?).
But if the mistake is "in the past" then just you being you day-to-day could still be repairing the damage (if it can be repaired) afterall you're showing them each day that you're not doing it or anything like it again.
And if there were extenuating circumstances make sure they know about those and how you're making sure that they don't lead you to making the same mistake again. Also make sure they know exactly what you've learned from all of this, e.g. why it won't happen again.
It does sound like your mistake has hurt them, but the best you can do is maybe try to support them with that, do you think??
Alison