I'm interested in the advice you have to offer as someone who has weathered a few relationships. It seems to me that the sex would always have to "go bad" as a relationship "goes bad", but the sex "going bad" would not necessarily be the reason why the relationship "went bad". I wonder about this because my H had only 3 lovers before we married and by his own report, two of them left him because of his low desire for sex. These were both relationships that only lasted a matter of monthes. I understand that relationship problems can "break" someone's sex drive, but don't people sometimes show up in relationships with sex drives that are already "broken"? I think this makes a subtle but important difference in how the HD partner needs to proceed. OTOH, the HD partner needs to do their share of relationship "fixing" in order to directly fix the sex problem. OTOH, the HD partner needs to do their share of relationship "fixing" and "fix" the problems that they brought to the relationship in order to encourage the LD partner to fix the sex problem that they brought to the relationship.
If I primarily blame relationship problems for my H's LD then this is the same as primarily blaming relationship problems for the fact that I became overweight. I was thin when I married, but I came into the marriage with a certain genetic and psychological makeup that made me prone to seek out food in reaction to stress resulting in an unfortunate effect on my figure. To the extent that I blamed this problem on my married childbearing state or my H's lack of support or any random stressor that popped up, I was unsuccessful in taking off the weight. I had to recognize that I was a person who had to work hard in order to overcome lifelong tendencies and lose the weight. This is not a problem that just magically goes away.
I think a person who comes into a relationship with a tendency towards LD reactions has a similar sort of problem. If they want to have a healthy active sex life they need to take personal responsibility for dealing with stress and "thinking sexy" in the same way that I had to take personal responsibility for dealing with stress and "thinking thin". I think the HD partner's role in this process should be the same as the naturally thin spouse's role.
1) Encourage weight loss but don't take responsibility for your partner's weight or weight loss plan.
2) Make it clear that you love your spouse but your strong preference is for a thinner partner.
3) Don't get too excited at the first signs of weight loss or too disappointed at the sign of a backslide. New habits are hard to learn and it isn't necessarily a linear process.
4) Remember you are free to decide at any time whether you are willing to stay in a relationship with someone who is unhealthily overweight (especially if "overweight" really means "LD" and your own health is affected directly). Think about your preferences and your priorities.
Sorry for the digression into yet another analogy. I guess what I'm trying to say is any sort of habit or tendency such as overeating or drinking or LD or the clingy form of HD can be seen as an "immature" reaction to stress or emotional upset. You are hurt or frightened so you need to have a cookie or a bottle or pout alone in the corner or throw a temper tantrum or clutch at your "lovey". The important thing to note is that the things we are seeking in such immature ways are things that we do need in our lives such as physical nourishment, personal space or recognition and physical intimacy, we just need to figure out how to seek them in a mature and balanced manner and allow our partner's the freedom to do the same.
"Tell me, what is it you plan to do with your one wild and precious life?" - Mary Oliver