Plex is „optimistically“ displaying the remote access status as available while it’s testing the status. That seems to be causing a lot of confusion… long story short: if the status indicator keeps switching from green to red after a few seconds you should assume it wasn’t working to begin with.
Did you already have a look at the related troubleshooting support article?
There’s also a guide with some more details on how to troubleshoot remote access issues. If those steps don’t lead to a fix, the individual outcomes will be helpful to further investigate.