What happens to grandparents in the Harry Potter universe?

We were all (re-)watching the Harry Potter films over the holidays, and at some point I suddenly noticed something I’d never paid attention to before: There are very few old people, and in particular almost no grandparents in the wizard world.

The old people we see are mainly school teachers (like Dumbledore and McGonagall) or authors like Bathilda Bagshot, and they’re all single. The only prominent grandparent I can think of is Neville Longbottom’s grandmother (and she’s of course a widow).

At the same time, it’s clearly the case that wizards and witches have children at a very young age, typically starting in their early twenties. In other words, the grandparents that are missing aren’t old at all (they should be in their late fifties or early sixties when their grandchildren go off to Hogwarts for the first time).

So what’s happening? Here are some possibilities:

• Perhaps magical abilities wear out the body quickly. That would be biologically plausible, but it doesn’t explain why unmarried wizards and witches can live for a long time, perhaps longer than muggles.
• Maybe older ones get clumsy and die due to magical accidents (a bit like the way Luna’s mum died). Again, it doesn’t explain why the ones who remain single can live so long.
• Another possibility is that it’s the magical equivalent of a midlife crisis that kills them, either by making them kill each other or by committing suicide. But again, why should this only affect married couples?
• Perhaps the children murder their parents a few years after having their own. I’ve no idea why they would do this, but it would explain why the childless ones survive.
• An intriguing possibility would be some sort of slow-acting magical STD that kills people around 30 years after having sex for the first time. Again, this would fit a lot of facts, but perhaps not how Neville Longbottom’s granny managed to survive.
• Finally, it could be that there is some sort of magical retirement home that is so wonderful that nobody who goes there ever wants to come back. Perhaps the children need to pay for it, which is why the ones without children cannot go.

I’m not really sure which option I prefer, and it is of course much more likely that Rowling just thought that grandparents would be an irrelevance to the story.