Marriages can have patches like this. All it seemed to have been is that she has lost sexual intimacy with him which caused a down turn in their relationship. Nothing that can not be overcome.
Additionally, that can be because of him, and not her. He stops putting in effort, so she feels less liked. Because she feels he doesn't like her, she's not so keen on being intimate with him because no one really wants to be intimate with someone who dislikes them.
But, then becomes a vicious cycle because she's now not being intimate with him, so he doesn't feel motivated to put in any effort...and so on. Round and round.
As you said, it can be overcome. Both need to put in the effort, and it needs to be a conscious decision. Just one party subtly making little changes isn't enough.
in chapter 3, the wife is talking to her cousin (MC's coworker) on the phone.
Her cousin mentions how MC is currently a project manager and is being relied on more and more at work of late, and the wife, unprompted, just replies with "aren't they just making fun of him?~" and she says it with a smile on her face while laughing.
This reads as way more than just her "being turned off sexually" by her husband. She literally kicks him when he's on the ground & in the middle of their floor after his first time at the gym, yelling at him for being slow and in her way, not once asking if he's actually alright.
She constantly admonished him for his appearance and age and "lack of usefulness" throughout their interactions in the first two chapters.
They have separate beds. Sure, that could be due to differences in sleeping habits, but on top of everything else and the fact that she shuts him down with a "you're an old man, stop acting like this" when he tries to be intimate with her, clearly shows she has no qualms about shutting him down and shutting him out, or having actual concern.
And the MC tries his best, at home and at the office, and everyone walks all over him in both places, including his kouhais, which is extra telling given how important hierarchy is in the Japanese corporate social scene.
If it's a matter of "their marriage is having a rough patch", it's pretty clear from the first three chapters at least that the wife is the problem here, with the only apparent issue on the MC's side being his lack of confidence due to all the putdowns and neglect he's received simply because he's a middle-aged man who isn't super physically fit.
This seems like you're giving Kuroudo a free pass when he isn't deserving of it. In relationships, things are rarely entirely one person's fault. Just because Kaori isn't being nice to him doesn't mean that he didn't do anything to deserve it. There's joint burden on both Kuroudo and Kaori.
Recall chapter 1 and the summary premise: Kurouda has been apathetic, dull, and unreliable for years. Kuroudo's not just a middle-aged man who's got a bit of a tummy now. He was, until recently, the epitome of a useless person.
He didn't start putting in any effort until he
unwillingly became a project leader, and didn't start a healthy lifestyle until being
blackmailed by Ayase. That promotion and what his coworkers said about him gave him a nudge to start actually trying to be proactive at work. Then, the blackmail actually forced him to start taking care of himself. Neither of these were because of his own resolve. He would have continued being useless and being a burden on his family and coworkers without both of those triggers.
It then makes sense that Kaori would ignore her husband's complaints and that she would not be excited to have sex with him. When she's talking with her cousin, the tone reads more like she's laughing because she's surprised or taken aback, not because she's deriding her husband but because of his character doesn't match the position. She may even suspect that he's actually getting promoted to window sitter. She certainly doesn't expect his coworkers to have nice things to say about someone who has proven themselves useless. Ultimately, they change topics immediately, so Rai doesn't get to set anything straight. Yes, it wasn't nice to not defend him or pick him up off the floor...but it's hard to blame her.
Even though he's now trying his best, he's only been at it for a few days. That's not enough for anyone to ignore years of uselessness.