Thanks for using our answers forums. We are sorry to hear about your issue with the video going black. Are you using an HDMI cable anywhere in the setup in the cable box, Slingbox, or TV? It sounds like you may be running in to HDCP, which is a form of copyright protection coming from the cable box. What you would need to do is remove all HDMI cables and use component cables as a passthrough.
Hope this helps,
The Sling Moderation Team