It is a known issue with the Android TV 9.2 client. Plex is aware of it and working on a fix.
Edit: In 9.3 beta, released earlier today.
Log out / Log in on the Plex Android TV app. That will re-establish the connection with the server.
You may want to hold off on re-pinning the libraries until a fix is available. Alternately, you could sideload the 9.3 beta or 9.1 release on your TV.
Uninstalling / re-installing Plex Media Server on the Synology is not required.
Another thread on the topic: Nvidia Shield - Pinned source disappear when Plex server is unavailable - #29 by DeanA320
