Should you stay in a relationship with a cheater?

Maybe. If your mate has cheated on you once, expressed profound remorse, participated in counseling and convinced you that they will never be unfaithful again; you should possibly consider giving them another chance if you you love them, can forgive them and are willing to do the work necessary to move on. If, however, any of the aforementioned conditions does not exist, cut your losses and dump the cheater.