Once you've setup the Slingbox for viewing locally, its the routers responsibility to allow remote viewing. I recommend that check your router's firewall rules. You'll need to make sure that that the corresponding public UDP and TCP ports and being forwarded to your Slingbox's private IP address. Most of the time this problem is associated by only having the TCP port forwarded.
Port Forwarding: http://support.slingbox.com/get/KB-2000068.html
Network Setup Assistant: http://support.slingbox.com/get/network-assistant.html
Manual Changes: http://support.slingbox.com/get/KB-5000126.html