You are probably running into a so called NAT loopback issue. I have a similar problem when I want to access webservices that run on a PC at home when I am connected with my wifi at home.
Many DSL routers/modems prevent loopback connections as a security feature. This means that a machine on your local network (e.g. behind your DSL router/modem) cannot connect to a forward facing IP address (such as 126.96.36.199) of a machine that it also on your local network. Connecting to the local IP address (such as 192.168.2.40) of that same machine works fine.
Is this on Android or iPhone/iPad? What I did was putting a proxy on one of my Windows machines. You can modify the hosts file on the machine so that a request to webservice.mydomain.com is forward to the ip of the PC running the web services.