It's up to two things imho,
A. Is s/he possibly going to do it again? and why did s/he do it in the first place?
I can think of a mistake, unintentional and not related to this person personality, so it's not likely to happen again, but if it was intentional or the personality itself is not honest, sincere, loyal and devoted, and perhaps going to do it again, so it's a no-no for me.
B. if A checks out (s/he's good, but made an honest mistake) so it's up to your forgiveness power and span, if you're able to really let go of that incident and totally forgive it, then it's cool, otherwise, it's not healthy for the relation to hold it as a leverage on your partner, to raise whenever you have a disagreement. If you can't let it go, then the relationship won't be healthy if you decided not to break up.