Does it click off and then back On?
The XPR has a local control sensor that maybe tripping back on from the TVs power supply.
The Appliance module also has local sensing but if it is a new design one. The sensing current is much lower and may not be tripping back on.
Test by putting a standard light bulb on the switched outlet along with the TV on the XPR. If it now stays off. The TV is tripping the local control sensor.
Let us know the results of the test and we may have some tips to correct it. One is a 7 watt night light on the same outlet.
One thing is kids are smart. I doubt it will take long for them to find out switching the thing off and back on again may again turn the power back on to the TV with the local control.
If it doesn't even try to turn off. Then I would suspect noise from the TVs Power Supply masking the X10 signal or absorbing the X10 signal. In that case an X10 type filter maybe the answer.
Just looked at the Installation Sheet for the XPR. Indicates that lamps or any load less than 40 watts may flicker or work erratic.
Sure sounds like it has a pretty stiff local control current.