I have the exact same question. I've been hoping to hear that a HDMI switch will solve the problem by providing some kind of "presence" output to the cable box, but I've been unable to confirm that this would work. I received the following in response to my query of an online retailer as to whether a switch would do the trick:
First, a little explanation of HDMI. HDMI is a format that offers two way communication between components. Some of the pins in the cable are for simply transmitting the audio and video signal, the rest are for data communication. The thing about HDMI is that different chips work differently, so it's hard to predict how they will react to each other. In the scenario you described, if the cable box and television are connected via HDMI, then when you turn off the television, it says to the cable box, "Hey, I'm turned off." The thing is the HDMI usually doesn't turn off. It's not that the cable box looks for the television and finds there is no television there as if it's been disconnected. With HDMI, the cable box looks for the television and the television responds, "Yes, I'm here but I've been turned off." The data communications portion continues to work. Just like on a computer network, you will notice that the LED on the NIC card stays on even when you shut down the computer. The network knows its still there.
The way an HDMI switch works is that the switch connects the data lines of all the connected components so that they are aware of the devices available on the system and switches only the video and audio transmission as necessary. At least that's how it looks to me from observing the circuit board and the way components behave.
If your television is shutting off the RF on your cable box it is actively doing so. You may need to physically disconnect the HDMI connection from the television to keep it from doing it.