Thought my space heater had died when I plugged it in and it wouldn't turn on, not even the "on" indicator light, so I went out and bought a new one. When the new one wouldn't work either, I tested the outlet and a lamp worked just fine. Carried the heater around the house and had no problem with the heater working in other outlets -- just not in the room where I want it!
The outlet contacts may be too dirty to carry a heavy load. Or they may be loose. Or the wires to the outlet may be loose either at the outlet or the in the breaker/fuse panel. I would recommend not using this outlet for anything until the point of cause is determined and corrected.