A .Net web service call throws a Network Without Access exception, but it’s still quite accessible

Question

I have a remote .Net web service that I added as a web link to my project via WSDL. When I try to call a method on it, I get the following exception:

A socket operation was attempted to an unreachable network 176.31.222.123:443 at System.Net.Sockets.Socket.DoConnect(EndPoint endPointSnapshot, SocketAddress socketAddress) at System.Net.ServicePoint.ConnectSocketInternal(Boolean connectFailure, Socket s4, Socket s6, Socket& socket, IPAddress& address, ConnectSocketState state, IAsyncResult asyncResult, Int32 timeout, Exception& exception) 

The address to which he is trying to connect is one of my own servers, and I can not only happily reach this IP address from my machine - other parts of the code that also connect to the same server work absolutely fine. This is only when using the web link to which it crashes.

Even stranger is that this does not happen on every machine, even between different machines on the same network give different results.

I'm pretty sure that something very stupid is going on that will make me palm, but does anyone know what is happening on earth?