In my ongoing saga, I have now swapped the console positions, which resulted in both consoles failing when they were in Location 1 (not to be confused with ID 1, which I am not using). Then I moved the IP data logger to the console at Location 2. Thereafter, the console at Location 1 lost communication with the external sensors, but the console at Location 2 (with the data logger) remained connected. I now conclude that there is some kind of RFI interference at Location 1.
The solution appears to be to abandon Location 1. I believe the interference may have something to do with the wall. I have a tonne of cables in the adjacent wall for a low voltage lighting control system that I control from my iOS devices. That wall also has iOS controlled thermostats and lights switches, as well as an Airport Express. However, I have used Location 1 for my Davis console for years without a problem so I actually have no idea what is happening.
Location 1 is very handy, but Location 2 appears to work and I do have access to the data through iOS.
So, for now, it appears that I may have a good workaround. Perhaps my transmitting board is not the culprit after all. I'll be back if I get disconnected at location 1. In the meantime, sincere thanks to everyone who chimed in here, as well as in Edouard's companion thread on a similar issue.