I thought that's what I did - the same problem does not occur with my other computers on the same network with the same router settings and more or less identical programmes. The internal IP address for the plug stays the same and the DHCP settings are set to infinite lease time.
I had a closer look at the plugs network behaviour, and it looks like there is no apparent pattern. The network is sometimes up for 6 or more hours, sometimes only for around an hour. I don't think it's related to the time of the day either, it appears to be random.