On Brad’s instruction, I disconnected everything from the network, leaving only a laptop (for ElkRP2 use with a wired connection) and the XEP.  Elk RP2 connected well and stayed connected.  I then brought each device back on the network one at a time starting with wireless, as I considered those more unlikely to be the cause of any network disruption.  I paused between devices, monitoring the connection between the laptop and the XEP.  It remained stable.  I then did the same with the wired connections, but stopped when I had connected all my known/labeled cables.  The connection remained solid.  I now suspect a bad cable or connection on one or more of my unused runs.

New ping data looks great…

Packets: Sent = 10, Received = 10, Lost = 0 (0% loss),
Approximate round trip times in milli-seconds:
Minimum = 2ms, Maximum = 4ms, Average = 3ms

I consider this resolved.  Thanks, All!