The Slingbox is so you can watch and control whichever cable box it's connected to. It doesn't act as a separate cable service. There's no way to "fix" that, as that is exactly what it's supposed to do.
Most people that are familiar with how a Slingbox works usually connect it to a cable box that isn't used as often. If you connected it to the main TV everyone uses, then that would definitely cause issues.