Here is a brief and very preliminary discussion of what politeness as a theory of relationship development might look like:
Among the theories of interpersonal relationship development are such well known entries as social exchange theory, social penetration, rules theory, uncertainty reduction, equity, and a variety of others. Politeness theory needs to be added to this list. It would go something like this:
Two people develop a relationship when each respects, contributes to, and acknowledges the positive and negative face needs of the other and it deteriorates when they don't.
"Positive face" is the need to be thought of highly, to be valued, to be esteemed. In more communication terms, respect for positive face entails the exchange of compliments, praise, and general positivity. "Negative face" is the need to be autonomous, to be in control of one's own behavior, to not be obligated to do something. In more communication terms, respect for negative face entails the exchange of permission requests (rather than demands), messages indicating that a person's time is valuable and respected, and few if any imposed obligations. It would also entail providing the other person an easy "way out" when a request is made.
Relationships develop when these needs are met. Relationships will be maintained when the rules of politeness are maintained. And relationships will deteriorate when the rules of politeness are bent, violated too often, or ignored completely. Relationship repair will be effected by a process of reinstituting the rules of politeness. Politeness, of course, is not the entire story; it's just a piece. It won't explain all the reasons for relationship development or deterioration but it explains a part of the processes. It won't explain, for example, why so many people stay in abusive and unsatisfying relationships. It's major weakness seems to be that politeness needs for specific individuals are difficult to identify--what is politeness to one person, may be perceived as rude or insensitive to another.
And, perhaps not surprisingly, politeness seems to be relaxed as the relationship becomes more intimate. As the relationship becomes more intimate and long-lasting, there is greater relationship license to violate the normal rules of politeness. This may well be a mistake, at least in certain relationships. Our needs for positive and negative face do not go away when a relationship becomes more intimate; they're still there. If the definitions of politeness are themselves relaxed by the individuals, then there seems little problem. There is a problem when the definitions--relaxed or original--are not shared by the individuals; when one assumes the acceptability of something generally considered impolite as o.k. while the other does not.
When people in relationships complain that they are not respected, are not valued as they used to be when they were dating, and that their relationship is not romantic, they may well be talking about politeness. And so, on the more positive side, it offers very concrete suggestions for developing, maintaining, and repairing interpersonal relationships, namely: increase politeness by contributing to the positive and negative face needs of the other person.