Hello,
I have the same problem with my PS4.
The Plex application works on all my media: Internet browsers, android phone, Windows 10, Xiaomi Mi Box S with the exception of my PS4.
The application launches, offers me to choose the user and then displays: The server “***” can not be reached securely. Do you want to allow insecure connections.
If I validate it tells me that the server is unavailable.
In the Plex settings, the “secure connection” option is “Preferred” (if I disable it, it does not change anything).
I specify that my Plex server is also accessible outside the local network and that it works without problems.
I guess the problem comes from the PS4 app. I looked for solutions on the forum and internet but I found nothing convincing.
My Plex server is on a Synology NAS.
Edit: I just came across this post: Suddenly unable to connect to PS4 which indicates that by replacing the default DNS of the PS4 by that from Google this fixes the problem.
I would not have the opportunity to test this manipulation before next weekend. I will then indicate whether it worked for me or not.