Thanks for getting to us here on the forums! In order to exactly identify and troubleshoot your issues I'd like to ask you a few more questions:
By turning off your TV, do you mean your physical television or just the video stream? Or do you mean that the cable box itself kept turning off?
Do you have any cables connecting your cable\satellite receiver to your TV or are you using the Slingbox as a passthrough? (Your TV is getting it's video and audio from the Slingbox itself instead of directly from the cable\satellite receiver)
If you could answer some of these questions for me, that would greatly help us out in identifying and hopefully resolving your issue.
The Sling Media Moderation Team