Yamaha won't be able to help you with this problem. It is not a problem with the receiver, it is a problem with the cable box. The HDMI switcher in a receiver is known as a repeater. When an HDMI connection is used there is a process known as an HDCP (High Definition Content Protection) handshake. The cable box is expecting to handshake with an HDMI receiver (such as a TV). It does not recognize the repeater as a valid device and therefore it will not allow the signal to go through.
As I mentioned before, this issue may be resolved with either a firmware update or simply a new box. You should try contacting the cable company.
Now, I will take a stab at one other possible solution, also a critical step. Have you assigned the specific HDMI input to the input you are using? For example, if you are using the "DTV/CBL" input and have the cable box connected to "IN2 DTV" on the back you will need to assign "IN2 DTV" to "DTV/CBL".
Go to "Input Select" in the receiver setup menu then go to the input you want to use for the cable box. Go to "I/O Assignment" then select "HDMI". Choose the HDMI input that you have the cable box connected to.