When I pull a plug from one outlet a TV plugged in to a different outlet on the other side of the room stops working.
When I put the plug back in the TV goes on... very mysterious

There most likely is a loose connection at one of the receptacles, need to pull each on the circuit out and check all wire connections.

You could have a loose connection in the outlet. When you pull the plug out, the wire looses contact and when you put it back in it makes contact. Pull the outlet and look for loose or burned wires, particularly if the outlet is backwired.