With respect, HDH, I'm not going to be happy in this relationship without intimacy. It's difficult to reach intimacy without having a sexual relationship. He knows nothing of my desires and fantasies or sexual tastes.
If we compromise and make an agreement as you suggest (we've done it before) he feels like he's doing chores and I feel like he's doing the bare minimum. It's mechanical and NOT intimate.
I know exactly how you feel, because I am exactly like you. I could not be happy in a marriage that did not include a mutually enjoyable sex life. That is partly because there is a dimension of love and connection that I can only esxperience through sexual connection. I certainly wasn’t suggesting that you settle for less than that. If it’s the case that having sex with you as much as 2-4 times a month feels mechanical and chore-like for him, and feels like less than the “bare minimum” for you, then it may well be that you two are just not a good match. I hate to say that, because I know how painful it is to hear, but there’s no point wasting time trying to “fix” something that can’t be fixed. The real point of my post was to alert you to the possiblity that his lack of interest in sex may not be a “problem,” it may just be who he is. If that’s the way he’s always been, and he doesn’t feel “wrong” or “not himself” when he is that way, then he’s probably no more likely to develop a high interest in sex than you are to lose your interest in it. You two are just different.