Open Plex in your browser by typing in http://Your-NAS-IP-Address:32400 and then go to settings->devices and delete everything except for the current browser session. Now stop Plex from running on the NAS.
Next, go to https://plex.tv and sign in if not already. Click on the 'launch' button and repeat the above, delete everything except for the current browser session. Then sign out of plex.tv.
Now go back and restart Plex on the NAS. Open Plex in your browser by typing in http://Your-NAS-IP-Address:32400 and then sign in, both in settings->server->general and by clicking on the 'head' icon (top right of screen).
Make sure you have followed the instructions above carefully, if you are still unable to access the server, then follow these steps but only if the above has failed, DO NOT try doing both at the same time:
Stop Plex from running, then open File Station and navigate to:
Plex/Library/Application Support/Plex Media Server and delete plexmediaserver.pid (if it exists) and Preferences.xml.
If you do not see the Plex folder in File Station, then see Q7a on the Synology FAQ's page, link in my signature.
Restart Plex, then type http://Your-NAS-IP-Address:32400 into your browser or click on the link in Package Center->Installed->Plex or from the DSM start menu->Plex icon and make sure you log in, both in settings->server->general and by clicking on the 'head' icon (top right of screen).
Hopefully, you will be able to access your server again.