Okay, so I’ve done some more tests, and this issue definitely seems to be configuration-dependent for me. As far as I can tell it’s VLAN-related.
Basically, what I’m seeing is that if there are more than one tagged VLAN configured on the same port, there will be no link on the switch after a hard power cycle (i.e. cable unplugged). However, connectivity can be restored without replugging, by issuing an /etc/init.d/network restart followed by a soft reboot.
The issue also seems to depend on what is at the other end of the cable. If I connect my laptop to any port, there’s always connectivity (to that port) after a hard power cycle. I’m not sure if this is also VLAN-related: The device that doesn’t get connectivity after a power cycle is a switch that only speaks speaks tagged VLAN.
For now I’ve worked around the issue by switching the WAN and LAN4 ports (so the tagged VLANs go out over the WAN port). This seems to allow me to reliably power cycle the device and get full connectivity.