Ok, terrible generalisation coming up:
Men need sex to feel close.
Women need closeness to want sex.
My marriage failed due to dysfunctional communication (and his cheating...). We'd lived sexless for a number of years, but the issue was low level resentment combined with the inability to actually talk about it.
I think your only hope is counselling IF he is prepared to engage with it - just going to the sessions without opening up is useless.
There's also a technique to open up clogged up channels of communication: every week set aside half an hour in which you both are undisturbed and not distracted (switch phones off, have children entertained otherwise, no TV etc). Each of you gets 15 minutes to say out loud what is on their mind, important and unimportant stuff, stuff at work, at home, with the neighbours, oh, the garage needs tidying, anything at all WHILE THE OTHER PERSON DOES NOT INTERRUPT OR COMMENT. After 15 minutes, it's the other person's turn. You can then agree to have another period to time to discuss together anything that came up in that half hour. You can also extend it to 2x15 min or whatever.
The vital thing is a. Opening up and b. Not interrupting.