When the ignition is off several electrical circuits on a car are inactive - i.e. the wipers don't work for instance - not until you switch the ignition switch.
All these supplementary circuits controlled from the ignition switch could have their power delivered directly from the switch but... that would mean a great big switch and lots of wires connected to it.
So - what car manufacturers do is have the ignition switch control a relay switch on or off and the relay controls power to those other circuits.
My guess is (and it's just a guess) that the relay in question is not operating.
You fail to mention your car make and model.
Good luck...
Peccavi, March 2013
