Yep, I've had similar issues with HD cable boxes from Comcast and Verizon. My current Verizon FiOS TV Motorola DVR is connected via component because of a similar issue.

Usually you don't need to turn everything off though, you can just change the input on the TV from current to non-HDMI back to what it needs to be and you should get signal.

There's no reason to use HDMI (at least that I can think of) to connect your cable box to the TV. Component works just as well and doesn't have all the headaches.