In most cases, the cable/sat box is set to AUTO adjust either resolution or the aspect ratio. Rather than having the cable box choose each time the channels are changed, you will want to go into the VIDEO menu of your cable box and set it to 1080i as a resolution and 16x9 as the aspect ratio.

If you need assistance with this, your cable provider would be able to help you navigate the menu if you can't find them. However, in most cases, this fixes the problem you're describing.

While the overwhelming majority of cable techs are definitely valuable and intelligent, this is a setting that can be often overlooked. I know it may seem like I'm asking you to do something with a box that you may not think is the problem, but that would be my recommendation based on feedback on the forums.