Update, if anyone is even remotely interested...
I'm now pretty certain it's a driver/BIOS issue rather than a hardware issue.
Lately, the problem was getting so bad that the external monitor was unusable, but I swapped out my regular laptop charger cable for one with an inline docking station. The monitor is now connected to the docking station via HDMI and the problem has not recurred since.
In the office the other day, I connected my laptop to the display in a conference room, USB-C to DP, and had exactly the same problem I'd been having at home, with the connection dropping intermittently for no obvious reason. Very annoying when you're trying to have a meeting with a number of people in the room and a number of people joining online via Teams.