The steam issue can be very simple. Steam just disconnects at some specific time, and dedicated server panics instead of gracefully continuing its work while trying to reconnect to Steam. Maybe this could be easily reproducible by manipulating firewall rules, if they can't afford dedicated server with external IP or can't make a deal with router administrator for forwarding them a few ports.

2 pc behind a router: 1 dedicated server and one client. Kill internet access to dedicated server (or just access to steam), and client will probably get disconnected from server.
By the way, it may be helpful if Steam is launched with "-tcp" parameter, which should improve reliability of connection.