Relationships are about compromise. In order to compromise, partners must exercise self-control in several areas of their lives. Spending habits, particularly when a couple shares bills, and the ability to remain monogamous in closed relationships are two areas in which a lack of self-control can destroy relationships. Without self-control, a relationship simply cannot survive.
Self-control is crucial in a relationship. Relationships take a lot of work on both parties involved and I believe part of that has to be self-control. It shows maturity and if you act on every impulse then the relationship will likely not last too long. Without self-control, trust issues begins to develop leading the relationship in a bad direction.