Just to clarify, you are able to connect while on the same network but as soon as you go to another network you are unable to connect to the Slingbox, correct? If this is the cause, it sounds like the network configuration is causing the Slingbox to not be able to leave the network.
This article below lists more possible causes and lists a few resolutions:
Sling Media Moderation Team
Originally, my iPad would connect in other locations with no problem. Now, I am unable to connect from other networks that I own and use to connect with no problem. I am able to access the device from other locations on my laptop with no issue. I have reset the device to factory settings and re downloaded sling player to no avail. Anything you can think of to configure my network correctly? I have the same router as before but can't remember making changes. This has to be a very minor tweak. I have sling player 500 and use the wifi. I am currently out of town again and can't try any troubleshooting until feb 18. Thanks