I think my (27f) husband (35m) is giving up

We've been married for just over a year, together over 3 years. We have no kids, just two dogs and live in a house with one housemate.
Pretty much since we got together he has been in and out of work, struggling with depression. I did the math and he's been unemployed for 30% of our relationship. I've really been there for him and tried to encourage him and make sure he knows I love him and just want him to be happy and stable, that I don't care what job he has as long as it feels good for him and he can stick with it for more than a few months. His parents helps him with his portion of rent, but I've been covering bills and food for both of us during the times he's been unemployed as well as 100% of the pet and miscellaneous household expenses pretty much 100% of the time. For context I run my own business and do pretty well financially so I can afford to pick up the slack, but it has prevented me from being able to save anything or work towards my own financial or personal goals, let alone take care of myself properly due to working so much.
For at least 2 years I've been requesting we do more together. We don't go on dates, he's expressed active disinterest in my hobbies and rejects every activity I suggest we try so I've stopped asking, although I always go along with his hobbies if he invites me, which is rare. There is no intimacy, much to my dismay, and hasn't really been since we moved in together 2.5 years ago. We have bad sex (no foreplay or aftercare) maybe once every 3 months and it's usually me initiating. He has no goals so there's nothing for us to work towards together even though I think it would really improve things and create a sense of teamwork. There's no tenderness from him, when we talk he is usually facing the other way or unable to look at me, or has a hat on shrouding his eyes. I've been trying so hard to get through to him but he's totally disconnected.
I'm finally at a point where for many months now I've been expressing that I can't sustain our current dynamic. I'm out of energy for this, just giving and giving while getting nothing back even when I tell him exactly what I need. That I need to feel connected, I want to kiss, hold hands, and have sex with him, I want to have fun and go on dates or just a drive or a picnic. He's a good person... we still laugh a lot together, but he can't have a difficult conversation without totally shutting down and rejecting me.
I told him last week that if something doesn't change I can't do this and that it's not fair. He's in therapy but won't try medication for his depression and won't do couples therapy with me. I don't have the tools or capacity to be the only one extending possible solutions. Lately the only time we spend together is having these long and painful conversations. We never yell, but there's clear frustration on both sides, and I don't know how to properly conclude a conversation like that so we usually just give each other a big hug after a long period of silence and try to act normal until the next one.
I want to fix things! I try to give him space, or check in with him and see what he needs but he can't articulate that, he says he feels like he's past the point of no return, that he's failed me, that he's incapable of love, that he feels like he has to be... "not himself" to make me happy, that he hates himself. I have never asked him to be anyone other than himself, just that I love him and want to have a relationship where we do more stuff together and have a stronger connection. I just want to find a common ground. I want to bring fun and romance back into our lives. It feels way too early in our relationship to just be living seperately but next to each other. I'm not even comfortable being close to him anymore but I want to change that. The thought of having sex with him makes me sad. We don't eat together, we don't watch any movies or shows, we don't even walk the dogs together anymore.
I'm not really sure what to do, if I should just let him go or if it's worth the anguish of being here with somebody who makes me feel so invisible.
TL;DR: My husband has been checked out due to mental health issues and I'm not sure if we can come back from it.


Source.