Why can I access my server on some public networks, but not others?

I can access my Plex server from most public networks, but not some, such as the one at the place where I do drug studies sometimes or at the apartment complex where I work. I am able to access my brother’s server in these locations, so perhaps it is an issue with my home router? I work for the company who runs the internet at the apartment complex, so I may be able to find out more. I do know they are behind a NAT, but I don’t fully understand what that means. What could be the issue here?

Some ISPs provide rather weak DNS servers which don’t resolve the .direct top-level-domain (reliably).
This is needed when the Plex server has set the ‘Secure Connections’ ‘required’ preference.
In such a case, the TLS certificate is ‘pinned’ to only the exclusive subdomain for your server which is is on the *.plex.direct domain.
If the router of the public WiFi cannot resolve this Domain name to a IP address, your plex client cannot talk to your server because it doesn’t know its IP address.

If you know the operator of the public network in question, suggest to them to switch using either Google’s public DNS servers or those from OpenDNS.
(These two have been proven to reliably resolve the .direct TLD)

The above is not needed if you use either an iOS or Android Plex client. AFAIK those have a workaround already built in.

The same also applies to your own home network, to some degree.

https://support.plex.tv/hc/en-us/articles/206225077-How-to-Use-Secure-Server-Connections

Thank you for response, Otto. I will look into that.