Lag could definitely be the issue. The authentication method is designed to have very quick timeouts to prevent man in the middle attacks.
Static IP for the server enhances reliability as this information is cached from Plex.tv.
With unreliable network settings, you basically want to setup your systems like they are offline.
On the Plex Media Server, set Secure connections to ‘disabled’ and add your local network to both ‘LAN Networks’ and ‘List of IP addresses and networks that are allowed without auth’. Also enable local network discovery.
On the rPi’s, multiple accounts are going to be the problem. If you use a single account and enable the preference ‘Auto Login’ the rPi will cache the authentication ID and just reuse it against the PMS without having to refetch it from Plex.tv each login.
See this thread for more information: https://forums.plex.tv/discussion/comment/1184504#Comment_1184504
It won’t solve all your problems forever, but it should make it more reliable.
