It depends on your car and the condition of your car.
In my experience, the 12V outlet/ cigarette lighter outlet on some makes and models of Toyota and Range Rovers that I've owned have had short circuits in the outlet themselves. So I don't have the full 12V out of the outlet. Normally, what this means is if the device does not detect a 12V source, then the threshold conditions aren't met and your device doesn't start charging.
Also, your car could have a faulty ignition switch. Usually, once you turn the car over the accessory power comes on. However if your switch is bad, it could break the connection to the accessory power you need to keep your GPS charged.
Why don't you consider trying to plug your GPS in another car to see if it charges while you drive? Maybe your GPS battery is on its last legs.