If the circuit is still live at the outlet, it is likely due to weakening of the springs that hold the plug in or a bad connection of the wiring to the outlet.
If the outlet is truly dead - no voltage on it whether a lamp or something works or not and no voltage in the wires feeding it - it is common to find it is GFCI protected, with the actual GFCI located elsewhere in the home. It is also possible that a poor connection on some other outlet is causing the problem; it doesn't need to be the one in question that is causing the actual problem. A splice in a wire nut, in the questionable outlet box or a different one, can cause an outlet to go dead.
Worst of all is a poor connection somewhere on that circuit. That will leave voltage on the outlet, but it won't work. Tracing such a problem can be a tedious task.