Point a web browser at the IP address of the Shield. For example, if the IP address is 10.1.2.3, use http://10.1.2.3:32400/web.
The IP address is visible in the Plex client app settings. It is overlaid in the lower right corner of the screen. You may need to turn on logging in the Advanced settings for it to appear. The IP address is also displayed in the Shield settings.
This is an ongoing problem that Plex has been unable to fix. There are multiple threads in the forum on the topic.
One recent post suggested setting a PIN on your Plex account in Plex Home settings: https://app.plex.tv/desktop/#!/settings/plex-home. Or, if a PIN exists, remove it, then force quit and restart the Plex client app (link).
Others have taken steps such as sideloading older versions of Plex Media Server, factory resetting the Shield, or reinstalling the Shield OS.
It is unclear if any of those steps are a lasting solution or if the problem will reappear. Hopefully Plex will figure out the root cause and resolve the problem.
Links to some of the other threads on the topic:
