I understand that when you are using your TV as the display for your Intel(R) Desktop Board DH67BL it works fine but as soon as you change the source on your TV and then go back to the HDMI you wont get any display until you make a change in the graphics options.
In regards to your inquire, the Intel(R) graphics controllers will not force an output like some video cards, to send signal thru a port, the graphics controller needs to receive a signal to notify that a device is connected. Now, it seems like your TV is not sending this signal when you switch the source. Another possible cause is the signal detected by the graphics controller when you change the source is not fully compatible and it stops the signal. You can try installing the INF file from the TV manufacturer or the driver if they have one. This can only be provided by the TV manufacturer.