Changing your Plex account password unclaims your Plex servers (removes them from your account).
To reclaim:
Option 1: Point a browser a the IP address of the NAS. For example, if the address is 10.1.2.3, use http://10.1.2.3:32400/web. Login to PMS, click the wrench icon in the upper right, see if you can reach server settings. If so, go to the General section and claim the server.
Option 2: FAQ 31: Reset / Reclaim PMS on DSM 7 (Not Authorized - Locked Out) (uninstall, re-install with a claim token).