Public static IP is not necessary.
Use a manual port forwarding statement in your router instead of UPnP.
The only port you need to forward for Plex is TCP/32400. Make sure it is not blocked by firewalls, etc (disable them for testing).
Check the box for “Manually specify public port” and leave it at 32400. If you wish to use a different port, then configure it in your router’s port forwarding statement.
The “Not available outside your network” message is at times a false negative. Use canyouseeme.org to verify if your server is available remotely. It will automatically pick up your public IP address. Put in 32400 (or whatever port you use) to check Plex remote access.
Once you have remote access working, consider using services such as uptimerobot.com (free) to monitor remote access. With the free account it will monitor availability as often as every five minutes and send you an e-mail if it cannot reach your server.
Port Forwarding rule in my Asus router:
WAN settings w/ UPnP disabled:
