If one or both people are dissatisfied with the sex being had, the question becomes which aspect is more important, the sex? Or the relationship itself? If both people agree that the sex is less important, than it can be something to work on within the context of the relationship.
I had one relationship similar to what you described. We had been together a long time, had been through a lot together, but towards the end of our relationship he seemed to be placing a new importance on sex that had not been there before. He would compare our relationships to that of his friends, using their experiences as a way of convincing me that something about my sexual appetite was abnormal.
Trouble is, I never cared about how much sex his friends were having, I was making decisions for myself and no one else. And of course I tried to be attentive to his needs too because relationships are about compromise, so how he felt was just valid as how I felt at the time.
However, I think he was just assuming that the longer we were together, the more frequently we'd be having sex. That isn't a need to be fulfilled, it is an assumption based outside the reality of our relationship.
And unfortunately, he more he compared everyone else's experiences to mine, and the more angry he became with me about it, the more resentful I became. He wasn't considering my feelings at all, it was as if no matter what I did to try to help the situation, it was never resolved. It seemed he would only be happy if I gave him exactly what he wanted, regardless of how I felt about it.
And at that point I realized that we just weren't compatible. There were other factors to the break up of course, but this one frustrated me the most. If our relationship had been healthy and strong otherwise, it would have been something I'd be more eager to fix.
But given that he overlooked most of the other important issues we had (trust, resentment, fighting over nothing, etc.), but chose to take a stand on the sex issue? It was as if the relationship itself mattered very little, and if I just sexed him more all our probems would just disappear.
Not only that, but he blamed me solely for my supposed "lack of interest". Never once thinking that how he treated me might impact my desire to be with him.
I honestly feel that his attitude made me less and less attracted to him. Sorry but not sorry, I'm not gonna be guilt-tripped into having sex with you. And if that's the kind of sex you want? You've got bigger issues in play than my libido, sir.
Only problem is, I've been living alone for three years now. And although I feel much happier outside of that unhealthy relationship, now I WISH I had that offer for sex on the table whenever I wanted it. I just hadn't reached that point at the time, which is probably for the best the way I see it.
I just had to learn in time that sex with the wrong person, for the wrong reasons...just isn't worth it for me. Sounds cliche, but when the time is right, you just know it.
And if the person you are with places importance on issues that matter very little to you, it's time to take a step back and reevaluate your own priorities, and hopefully (if they're smart) they'll do the same.
Things don't always go the way we want them to, but sometimes that is necessary for things to go the way that is needed.