Here is one possibile issue you can check:
For More Information see:
Windows systems: FMP installer does not install server.pem file
This is one of many acknowledged bugs that can be found in the Known Bug List thread here in the Report an Issue section of the forum.
It can also be downloaded as a database file from: https://www.dropbox.com/s/jt09b82i0xijbu3/FMP%20Bugs.zip
I have uninstalled and reinstalled FMP. The file server.pem installs, and seems fine (shows as 5K). Maybe corrupt? Can someone post a copy for me to try?
You can try copying the file from one of the computers where they are able to connect to the database.
I tried dragging/copying the server.pem file right from the install package to my app. No joy. I can only assume my issue is related to something else.
But...here's an interesting twist!
I remembered that I have a "helper" file I created to make it faster/easier to access the hosted database. It's just an FM document with a script that connects to the remote DB (via the IP address), opens the files with the right password, sizes the screens to my preferences, etc.
The interesting thing is, while continuing to troubleshoot this, I launched the file at home just to see what would happen and it quickly accessed the hosted files (at work). Voilà!
So, at least I can use this as a work-around until I solve it (or the developers solve it). Unfortunately, none of the other solutions posted here have worked for me.