What could be wrong with this receptacle?
How exactly do you know that the power is going back on?

If the TV is still plugged into one recepticle and simply plugging the AC tester causes the TV to come back on ---- then you need to immediately investigate repairing and replacing the duplex recepticle. It is likely that the wiring in the box is using the quick connect type connection where the wires poke into a hole in the back of the outlet. One wire must be loose and making an intermittent connection. This could be caused by a wire that is improperly installed or the internal string contact that is supposed to retain the wire is broken. Simply installing the AC tester into the other outlet is apparently moving the contact metal work inside the recepticle just enough to cause it to touch the loose wire. 

Do note that a loose wire like this is unsafe and could lead to a fire - so please investigate immediately - for the sake of yourself, your family and your dwelling.