Is there something specific with that machine's configuration that may prevent wyUpdate to check for updates?
Yes, about a billion things (hence the generic message). My guess: a local firewall or proxy is blocking the connection to your server. You'll have to use WireShark to see exactly what's wrong with the connection. Also see if they can download the wyserver.wys file from a browser. If not, then there's something on the computer (e.g. hosts file, firewall, proxy, etc.) or something in the LAN (faulty hardware, hardware firewall, proxy, etc.) that's blocking the connection.