'It seems to me that if everyone refused to say when a monogamous relationship was over, refused to tell someone of their affairs, and so on, then no monogamous relationships could exist.'
I don't see that the conclusion follows, because it takes no account of monogamous relationships that persist and are not over.
'If relationships of these sorts were never obeyed, or clarified, they would not exist, right?'
I am not sure what work 'or clarified' is doing but if the requirements (whatever they are) of a monogamous relationship were 'never obeyed' then the relationship might continue to have a legal or formal existence but would not actually be practised. In this sense it would not exist.
'Even if they could exist as one off events in someone's life, they could not last, and it's difficult to conceive of -- not just will -- monogamy never existing twice in anyone's life.'
Uncertainty again: is this is meant to follow logically from your previous statements or is offered independently of them?
Let's start from Kantian basics. Does he privilege monogamy? Yes, quite clearly he does in The Metaphysics of Morals (1797):
The relation of partners in a marriage is a relation of equality of possession, equality both in their possession of each other as persons (hence only in monogamy, since in polygamy the person who surrenders herself gains only a part of the man who gets her completely, and therefore makes herself into a mere thing), and also equality in their possession of material goods. (Kant, The Metaphysics of Morals, §26, tr. M. Gregor, Cambridge: CUP, 2017, 68-9.)
How does this relate to Kantian ethics? Kant's argument (and his response to your question) is roughly as follows. It is in and only in a monogamous relationship that each person surrenders her/ his-self completely to the other. Each allows the other to own their person: X owns Y's person and Y owns X's person. From this perspective, neither will lose their own person and become a mere thing (something to be used as a mere means). Only so can the formula of humanity be respected in sexual relationships.
This seems a strange argument. How does X own and not lose their own person by owning Y's person and Y's owning X's person? How can I own myself and be the property of another?
Kant's response, or at part of it, seems to given at §25. In mongamy (which he clearly has in mind in view of §26):
one person is acquired by the other as if it were a thing, the one who is acquired acquires the other in return (Gregor: 68).
How to justify the 'as if'?
That this right against a person is also akin to a right to a thing rests on the fact that if one of the partners in a marriage has left or given itself into someone else's possession, the other partner is justified, always and without question, in bringing its partner back under its control, just as it is justified in retrieving a thing. (Gregor: 68.)
But if X brings Y back under X's control (this relates to infidelity in your question), we are still in the paradoxical situation in which X owns and does not lose their own person because X owns Y's person and Y's owns X's person and the question remains (to repeat): How can I own myself and be the property of another?
My suggestion is that you are right to raise questions about what one might term the moral logic of Kant's account of monogamy but that the real problems about that logic are located elsewhere.
I. Kant, The Metaphysics of Morals, tr. M. Gregor, Cambridge: CUP, 2017.
L. Pakadaki, 'Kantian Marriage and Beyond: Why It Is Worth Thinking about Kant on Marriage', Hypatia , SPRING 2010, Vol. 25, No. 2 (SPRING 2010): 276-294.
C. Korsgaard, 'Creating the kingdom of ends: Reciprocity and responsibility in personal relations', Creating the kingdom of ends. Cambridge: CUP, 1996: 188-221.