It seems to me that this impasse develops when one partner considers sex to be the building effort and affection to be the maintenance, while the other one considers affection to be the building part and sex to be the maintenance.
During the building phase, both are working hard and both are getting both sex and affection. But when they reach maintenance, suddenly one partner feels sex is less important but the other feels affection is less important.
Unfortunately, it's usually men who use affection to court women, and women use sex to court men. Like you said, both usually reach the maintenance phase and can fall by the wayside.
You know, it's funny. Both men and women have the same complaints, especially after marriage.
"My wife used to have sex all the time, and now it's a chore!"
"My husband used to be SO affectionate, and now he can't be bothered!"
It's the same issue, isn't it? The same complaint.
The go-to "solution" for this is usually logically, but rarely seems to work: Be more affectionate, and she'll have more sex with you. Have more sex, and he'll be more affectionate with you.
As somebody in this thread mentioned, it doesn't work for him. And I am in the same general boat as well.
I find that, at least in my experience (and I do need to be careful here...) that when men purposefully become more affectionate in the hopes that their own needs will be met (as per the go-to advice), the woman often tend to not believe they are doing it for the "right reasons". As in, they don't quite trust their husband/partner is truly showing them affection for anything more than the goal of having sex. They may feel manipulated.
Whereas, I find when a woman becomes more sexual, with the goal of receiving more affection, we men are pretty quick to accept and reciprocate.
I know I feel MUCH more affectionate about my wife when she makes an effort with something, especially sexual. The effects usually last for days, as well. I don't quite understand why she hasn't figured this out, either, even after basically telling her this bluntly. But more often than not, her efforts are few and far between, and she wonders why I've fallen off after x-amount of time. And I DO make the efforts to meet her needs even when mine are not being met, but there's often a finite amount of time for me to reach the point of non-interest because nothing's coming back.
Humans require motivation - it's that simple. Motivation has to come from BOTH sides, not just one, and not at a 10 to 1 scale, either. This scale can vary depending on personality. I'm a people-please, my wife is not. Therefore a 3-1 scale would work for me, for example. Every 3 things I do to please her, 1 in return for me. The scale will vary for everybody. Even 10-1 might work for some people.