Thanks for participating in our online forum community here! I do apologize for any inconvenience you're experiencing when trying to view your PRO-HD when your TV is turned on at home. We may need some additional information to narrow down the issue here, such as what cabling are you using from the cable box to the Slingbox and from the cable box to the TV? It sounds to me like the issue may be a SOC (Selectable Output Control) issue from your cable box.
Here is an article from our support site with some additional information regarding SOC:
Hope this helps!
The Sling Moderation Team