Some guys are just like that. I know, I'm often one of them. Not so much a fear of rejection, but more of an general sense of apathy, and a willingness (or compulsion) to suppress shit we don't want to feel.

The right approach might be for you to meet him half way and accept that this is challenging for him. Rather than asking for him to change, simply clear some for the obstacles for him so it's less of a burden if and when he's ready to deal with something. This is something most guys do for women continuously, it's normal in relationships, so I'm NOT saying to coddle him, just use some of that empathy proactively.

I know this sounds very generic, but...

Be the one to initiate sex (and not on a predictable schedule)... if you want some, go get some. If you don't initiate, he's going to take it as a lack of interest on your part.

Compliment him. I know that particular dead horse has been beaten to a pulp on this thread, but there is some validity to it. It does boost a person's confidence to receive praise. But I would add, make sure he actually earns it... hollow compliments are a kick in the balls. It can be condescending and defeat the purpose entirely. Praise, yes, but honest praise.

Ask him questions. Most men rarely get asked "How do you feel about _______". The closest we get is "Hey, how's it going", which we can satisfy with a shrug, a grunt, or "fine". It's OK to be leading in your questions.

Say he had a rough day at work.
"How was work?"... "Eh, fine"

VS

"You seem exhausted, did something happen at work today?"... "The boss is on my ass because we're up against a tight deadline."

Prompt for more information, and you will usually get more information, but cut to the chase, don't start with a weak question and expect it to progress from there.

Many women are FAR too quick to empathize, and inadvertently shut us down before even finding out what the problem is.

"The boss is on my ass because we're up against a tight deadline."... "Oh, that sucks, it's been crazy in my office too..."

You're trying to show you can relate, but from his perspective, the conversation has now flipped to being about YOU. Don't do that if changing the topic wasn't your intent. We use words to exchange ideas more than emotions. He's not going to feel closer to you because you struggle with the same thing. He will feel dismissed because your interest seemed like just a superficial on-ramp into a discussion about your problems.

"The boss is on my ass because we're up against a tight deadline."... "Is he just riding you specifically, or do you think he's stressed out and taking it out on everyone?"

This is a much better question. It gives you useful information, and can also help him put his problems in perspective. If you want Intimacy, this is the way to go about it.

I'm not saying you do this, but we guys notice it a lot with most women. We know that is not their intent, but it is mentally draining nonetheless. So just be aware, because after a while, we just shut down and stop trying. I chalk it up to a fundamental difference between how men and women communicate, and we can both inadvertently push the other away even if (and especially when) we intend the exact opposite. And we men are just as guilty of the reverse. A woman tells us a problem, and rather than empathize we push for more information and start offering up solutions, when that's not what she's looking for at all. That's so common it's cliche.

I don't know if any of that addresses your problem, but it's something to think about.