An increasing number of car manufacturers are working to maximise the fuel economy of the vehicle, and are fitting "smart alternators" which only produce power if the car or the car battery needs power. These systems often ignore the the trailer wiring and stops producing any electrical power in excess of its own specific needs. Consequently we are seeing more caravanners who discover their caravan batteries are not being charged as much by the car and fridges are not keeping cool.
It's also the case that many "standard" towbar wiring looms only provide for the trailers road lights, and you have to specifically request supplementary circuits for battery and fridge operations.
If your car has a "smart alternator" then check the cars user options which might include a way to keep the alternator working. In some cases the cars ECU needs to be reprogrammed. Check with your towbar fitter, and or the cars dealer or manufacturer.