I check the tyre pressures before going away but I have never had a problem with them dropping when touring.
Sam beat me to the short answer,
The reason why tyre pressures often need to be increased when towing, is partly due to the significant static nose load that is added to the car - especially the rear axle load, but also when the car accelerates, changes directions, or brakes, the caravan does impart much higher loads through the tow bar, which places considerably higher and loads in different directions through the cars rear tyres and can cause them to squirm.
The higher pressure not only helps to support the static loads, but it also stiffens the tyres side wall to reduce the squirming effect that additional side loads can produce.