Are those servers all in your own home network?
Most likely, it is an issue with your router. Or more precisely, with either the DNS server of your ISP or your router’s blocking of “DNS rebinding” attacks.
See Cannot find Server
If you have “required” Secure Connections in your server (which makes accessing the server impossible if your DNS doesn’t cooperate), you can reset that preference by double-clicking the ‘.reg’ file from this archive: secure_preferred.zip (374 Bytes)
Do this while the plex server has been closed and is no longer appearing in your task tray: 
