I think the next time he says "I don't think I can give you what you need" I might just agree with him and see what type of response that gets Some times that is what you have to do.
BB frequently answered my questions when we were at odds, with the question "do you want a D?" and she never got around to an answer to my question. Then I would try to smooth things over, calm things down, so once I said yes when she said the D word.
BB quit answering my questions with her, "Do you want a D?"
I think the "I can't give you what you want" is a bluff and an escape hatch for your H. It is a way for him to be non-committal.
I remember GEL telling her H "there might not be any more anniversary’s. I think that did a little something to get his attention.