What I'm getting from your post, is that you're having problems connecting from a different network than the local one.
Now, before I provide any response let me ask you.
Are you able to connect using a WiFi network, from the computer? Or you're talking about the connection from the phone also?
Besides that, we will appreciate if you can provide more information about this issue, for example, you can send information about error messages, network layout, type of phone, type of Slingbox, etc.
That way, you will be able to provide a proper response.