Thanks for all the power supply suggestions, but at this point I'm convinced there is nothing wrong with 3D2AG's power supply (he may have been hearing the fan speed change in the NUC).  With Skimmer terminated, I tried copying a large file from Windows to the RP using the SCP command, while monitoring the Network throughput using the Windows Performance Monitor.  The copy works for a little while, and the transfer speed peaks at about 135 Mbps, then the SCP command seems to hang for a few seconds, and then it aborts and reports "broken pipe", and the Ethernet connection to the RP is reset (one of the RP's LEDs goes out, then comes back after a little while).  I repeated this a few times, and it stopped at different points, so it has nothing to do with disk space or with SkimSrv, just network performance.

Bottom line:  as soon as a large amount of data is being transferred from PC to RP or vice versa, it only works for a short time, then the connection is dropped.  We've tried different cables, and using the Router as a switch, and using a separate standalone Ethernet switch, and it made no difference.  This same configuration has been working OK for months.

Antoine noticed that the RP heat sink was not solidly seated (the white plastic tabs that hold it against the chip were apparently not pushed in all the way).  So perhaps this chip has  been overheated too much, and now is only marginally functional.  He reapplied thermal paste and properly seated the heatsink, but it didn't make any difference, and xadc reports the temperature is OK.