I think that sex can be pretty broadly defined, and for me that also includes physical intimacy. You may not be fucking like bulls, but cuddling and kissing have to be there, at least to my mind. I don't think you can have a relationship without kissing and touching and holding. And I think that there has to be some release, whether mutual masturbation or frottage.
If you're looking at extremes - such as a dying partner, a critical illness, then circumstance necessitates a shift, and yes, you can still be in a relationship with that man. You better be! But I don't think your question is about extremes.
I've transitioned out of an LTR when intimacy was a waning and finally altogether absent reality for my partner. We stayed very deeply connected friends. The reason was partially a drop in T'count, and his lack of desire to address it. He was happy, truly happy being non-sexual and non-intimate. I, was not. And rather than grow resentful and frustrated and hurtful, we adjusted to a shift that closed the 'partner' or 'husband' door. And we looked LONG and hard at options, and counseling and difficult conversations. It was NOT easy, but it was healthy and respectful. And it lead us both to the conclusion that we were not longer a couple.
I like being coupled. I crave it. And physical intimacy is a key factor in being coupled happily. It is not the primary driver, but attraction, and the expression of that in tender and passionate ways cannot be missing, or things feel very out of balance.
Now, there will come a time, I'm guessing, when I will not have the same drive for sex per se, but I cannot imagine a time when touching, and holding, and kissing are not a truly critical form of how I express myself and connect to my partner/mate/boyfriend.
I believe that without it, you have a very nice friendship, but not a truly intimate relationship.