The problem is mostly solved.
1) I replaced the wall transformer at my home QTH with a cable to the station's main 13.8 volt power supply that I mainly use for my IC-7300. The wall transformer was only supplying 12.0 volts. For safety reasons I put a 1 ampere fuse in the cable. Now the system is powered at both sides with 13.8V from linear supplies.
2) The link between the two RemoteRig units had 7 hops according to the software PingPlotter. I replaced it with another link with only 4 hops. The new link uses a high speed (100 Mb/s) service at the local QTH, and a 4G router (40 Mb/s up and down) at the remote site. Both services are run by the same company
www.siminn.is so interconnections are short and few.
My RemoteRig + TS-480 setup works now almost perfectly. I have not experienced any dropout.
The only quirk is that when I turn on the TS-480 rig with the power on/off button the red light appears on the RemoteRig. Usually the HELLO greeting appears and freezes. Then I wait until the red light turns off and press the power on/off button again. This usually is sufficient to wake up the Kenwood. In some cases I have to remove the 6 conductor plug for a second from the TS-480 control head, and everything remains OK after that. It seem to be something related to the serial connection between the RemoteRig box and the TS-480 control head. I can live with this minor quirk until I find a solution.