(This is jeopardy-style; I found the answer eventually, but it is not what I expected. Posting here for search etc).
I have a Dell laptop and external monitor (on DisplayPort). It was fine for ages, but recently it has started cutting out randomly, displaying "no signal". Turning the monitor off and on, or disabling and re-enabling via Windows both make it work again, but it is annoying and disruptive.
To investigate, I've disabled all the power settings / screen-saver / etc, so it shouldn't be the OS disabling it electively.
What might cause this? And how can I fix it?