the site uses an http server, which logs the incoming connections. at work you probably have some sort of a Tsomething connection, or some other kind of static IP connection. Those might be filtered by the server as safe/stable/etc and the connection timeout would be long.
as for dialup/dsl/cable ip addresses, the server might shorten the connection uptime, since those are often used by spammers, or simply because those addresses change a lot.

what I would do is try to contact the game's support, give them your details, including the tracert, and ask them to help you