This is a great question, but I would first have to state that I don't believe there is a definitive way of resolving it—as with many issues in literature. It is true that May keeps her silence, but in her last exchanges with Marcher, she reveals enough for us to understand more of the dynamic between them than had been revealed to us through their relationship up to that point. Still, what she reveals is ambiguous. The core of the matter is that although these two have, indeed, had a relationship of a kind for years, we do not know what the actual basis of it has been. Is it mere friendship, or is it a kind of platonic romance? Is it more than platonic, though they never act on the implications of it? Is it some kind of mystical bond that cannot be explained in ordinary terms most people would understand or could relate to?
The only thing that comes through clearly is that there has been something deeply unsatisfactory and unfulfilled in the connection between May and Marcher. Her final illness and death are symbolic of her misfortune in having been attached and devoted to this man who has offered her nothing concrete, a man who has had a lifelong, narcissistic obsession with both an inner demon and the outer Beast he believes has been lurking for him, waiting to destroy him. In the end, Marcher himself realizes that his attachment to May has been a monumental failure, that upon her death he has less claim upon her memory and legacy than "a fourth cousin" of hers would have.
I would disagree with the implication in your question that it is May's silence that has doomed both of them to unhappiness. In this story, as with so much in James's oeuvre, the most decisive points are couched in riddles, stated indirectly or left for the reader to infer out of a mass of detail and observation that is reported to us in elegant language—language that deliberately prevents us from coming to definite conclusions about the characters' inner motivations. As is the case even in James's earlier and much more straightforward Daisy Miller, we somehow feel that the central lives in the story being shown to us are behind a veil. The overall point may be that this is the way most of us appear to other people, as if no one can ever fully understand another person's inner nature.