Just a thought and cant remember the technical termanology but remember that propane uses warmth to produce the vapour and in very cole weather you may not get all the gas out of the bottle if your usage is high. Pour some hot water over the cylinder and watch the difference. 
Good point. You have to boil the propane off the liquid in the cylinder. If you're using it at a high rate under cold conditions there might not be enough ambient heat to do so. Usually the cylinder will frost up in that case as the boiling liquid extracts heat from the environment (a good way to tell how full the cylinder is - try feeling for the liquid level if there's no frost / condensation). Propane is not too bad in this respect though. It boils at -40 deg c under ambient conditions. Butane is a real pain in the cold though.
I have experience of a central heating system that was fired by 47Kg propane cylinders located outside and never had problems with the cold. I'm sure we saw temperatures down to -6 or 7.
Another possibility: do you have an automatic changeover valve that selects the cylinders automatically? Could it be that it's switching over early so you're changing cylinders prematurely? Could also be related to icing, since the pressure will drop off if the cylinder ices up.
Kevin