Update to this thread for historical accuracy! The disconnect happened again after my last post a few days ago. So I did more detailed troubleshooting and gear swapping. In the end, I was able to trace the whole problem to a failing switch on my network. The switch would work intermittently after power cycled (which I did several times in the course of trying to resolve my issues documented above), but would always die again at some point in the next 24 hours, so I would find the duet disconnected again.

I replaced the switch and all is well. So it turns out my ire was misdirected at the squeezebox duet, and I am still a big fan!