Yikes.
In my experience, a single man is almost Never Shunned.
Oh, I don't know.
Okay - so to tackle the topic..... no easy answers. A lot depends on the illness, and the overall impact it has. We should also account for what it's possible for us to do. For example, if your partner needs turning every two hours, and you are yourself ill - say with arthritis - then it may simply be a case that you're not able to help. It's beyond your capabilities.
While it is within your capabilities, then I'd suggest us old fashioned folk feel a responsibility to do the caring.
Divorce? Over an illness? The only time this would be okay, for me, is if it's needed legally. So for example, if getting divorced means local state services step in to help care, then I can see it. But as a matter of convenience? That comes across as being a little cold.
We all age, we all get decrepit. We know this when we're young but don't pay it a mind. But the day inevitably comes. The worst my family has experienced was fairly recently, when an aunt suffered from dementia. You can care for the person for a time, but there comes a time when you just can't (just me experience).
There's probably no definitive answer to such a question.
I have commented only from a practical standpoint. While there may be pressures in the relationship beyond practical, I do think that's what we sign up for. But then, I believe in marriage and what it means and stands for.