Replying to myself after more research.
This problem sounds vaguely similar to this thread: Debugging Homematic IP: no updates on some HmIP devices after some time - #13 by haukman
However, that says that it is fixed in 3.1, and I’m on 3.1.0-1, so presumably I have a fixed version. Having said that, I did just run an upgrade two days ago, before that I was on one of the release candidates for 3.1. Perhaps this fix didn’t go in until the final 3.1?