Punctuation is your friend. So, are you saying that when the tv is powered on the cable box stays on and functions normally but when you power off the tv the box powers off and then reboots when powered on again?
Can you describe how the box is connected to the tv? HDMI, coax, component/composite cables? Is the box power cord plugged into the wall socket or an outlet on the tv itself? Is the tv power cord plugged into the switched or unswitched outlet on the back of the cable box?
Turn off the CEC for that port in the tv or connect to a non cec hdmi port...
This is also an issue with some directv to tv boxes... It is a TV manufacturer issue .
See if the box has an option to turn off CEC
Or use a hdmi to DVI cable with a dvi to hdmi adapter to convert it back. That strips off pin 13, the CEC pin