Personally, from experiences I have been through, trust is everything and without trust there is no relationship. Once somebody has thrown away my trust they don't get to earn it back. Clearly it doesn't mean that much to them.
However that's me personally. I know plennnty of couples that have had a bad breakup after a mistake and then get back together and they're happy as larry now...even though at the time of the mistake they were insistent it could not be fixed and it was over.
I find it more difficult to trust people once you've been taken for a mug repeatedly.