Plex Remote Access Intermittently Turning Off and On

As others have stated above:
The way the remote access status indicator works is it’ll show as „green“/working while testing the remote access status. This is by design. You can argue if that makes sense or should be improved (e.g. by showing a 3rd state like „checking status“).

If you experience the remote access status indicator showing „green“ for a moment (even up to a minute or maybe 2) and then switching to „red“/not working → assume it’s not working in the first place.

I’m not aware of any current or newly introduced server side issues with remote access. Usually those issues come down to some aspect of the remote access setup being broken… ranging from your ISP‘s backend, your router, home network, server OS (incl. local firewalls or security tools) to a bad configuration of remote access inside the Plex Media Server.

If you want to troubleshoot remote access issues, it’ll be helpful if you can look into what part of that chain is giving you trouble (potentially there’s more than one).
This guide is usually a good place to start… if it doesn’t help you to actually fix your issues, the respective findings might still be helpful to anyone who’s going to assist you further.