It's a great reason for this AMA.
I've seen a lot of discussions about dead bedrooms. The vast majority of advice is to always look into health and stress.

Then I have the hottest tip for you. Try MDMA with your husband. This substance aids with difficult conversations and is being researched as a solution for couples therapy.

I have tried this with my partner. You will have a conversation full of love and empathy, there will be 0 judgement and embarrassment. No matter how difficult the topic. You will feel heard like you have never felt before. This is almost a 100% guarantee.

MDMA has saved many marriages just because it facilitates deep conversations. Look up some of those experiences online, many couples will be very vocal about how MDMA saved their marriage.
Now that's just the communication benefit of it, it's also a new fun thing to experience, something to push both of your boundaries, and it can feel very very intimate and sensual, even when actual sex doesn't happen.

Feel free to DM me if you have questions that you don't want to ask publicly. I am 100% confident this will help you both,

That was then. Please don't give up on this! <3

I've backed out from a few threesomes myself, and I'm grateful that my partner keeps trying. I just was not ready at the time.

I would urge you to clarify as that would tell you if he has lost his urges completely or not.
From your replies, it sounds like you guys could work on your communication as well. You are working with a lot of assumptions.

Mental health = physical health. Stress and tiredness = medical, my lady friend. Prolonged stress can have exactly this consequence that you are describing.

I would urge you to push him to check his testosterone levels and overall health. It is the obvious answer and the no. 1 thing to check here!
If you guys are not willing to look into his health then I really wonder if this is such a big problem as you make it out to be? Sorry, it's just frustrating to read that this is such a huge problem for you but you have not been to the doctor because you "don't think it's medical".

Could it possible that he would be interested in simply watching you enjoy another woman?
I would encourage you to keep bringing this up with your husband. The fact that it didn't work out that time, doesn't mean it will not work out again.
You need to keep bringing this up because 1) he should know how this affects you and 2) he may have done some reflection on the topic himself and may have different opinions now. You may notice he now gives different reasons for his opinions, and that just opens up the conversation more.