Can they connect to a different network (EG local coffee shop if they're on a laptop) and diagnose if maybe it's a piece of network hardware in the building that's kicking off the connection?
My network IT skills are a little rusty, but you might also run something to check and see if any other program is listening for port 5003. Sometimes you can get a conflict where a secondary program is responding on the same port and kicks off the original program.
I believe on windows command line it's:
netstat -ab | more
and OSX terminal:
lsof -n -i4TCP:$PORT | grep LISTEN
Yes I am pretty certain its some type of firewall latency or something internally, its a local government so getting their laptop out of the building to try elsewhere could be off the cards.
I do think it is their own problem and I think Ill leave it with their I.T dept.
Nothing else listening on that port..
I've dealt with those types too. best to let their IT department sort it out as well and just give recommendations (and proof that it's working for others outside of their network).
Might want to offer the IP or DNS address of the server so they can whitelist it. Also, make sure they don't have NAT turned on that's redirecting port 5003 anywhere else.
I have been suddenly having this issue within the last few weeks of first one, then two computers losing communication with host constantly, sometimes every several minutes. So far I have
1. Uninstalled and reinstalled FM.
2. Recovered database
3. Had the ISP test wi-fi and individual computers ping, all in perfect shape.
I do not know what to do, and filemaker support did not have any further suggestions. I am suspecting that something in one of Mac OS updates (running Yosemite) has become incompatible with FM13. If I figure out the solution, I will post it here, as it seems you are having a very similar issue.