You must remember how propane works. The pressure in your tank/cylinder is directly related to the temperature of the propane. At 60F, the pressure is about 102psi, at 20F about 47psi and at -20F it is about 13.5psi. Propane at atmospheric pressure instantly goes to -44F and stops boiling hence no more vapor to build pressure. If you consume pressure faster than the propane boils, you will eventually fall below the regulator output pressure required to run the unit (about 10-14"wc or 1/2psi). This is why you see condensation or even frost on a propane tank/cylinder under a large useage load. Propane would be used for refrigeration if it was not so unstable and flamable.
What do you do when you need it to work? First thing is make sure the tank/cylinder is open to air and not in snow or insulated in anyway. The propane needs to be a higher temp than -44F to produce vapor pressure. DO NOT TRY TO HEAT A TANK/CYLINDER! PRESSURE BUILDS FAST (@100F, it is at 220psi) AND OPEN FLAME AROUND IT IS A BAD IDEA! THINK SAFELY PLEASE! My grandfather always told me that those that did not respect electricity were self eliminating problems. There are many many energy sources we can say the same thing about and propane is no different.
Try to decrease your consumption rate and if the unit stops functioning properly, the propane must find some safe warmth like the sun or just a break to warm up to the outdoor temp. Even if it is -20F, once the propane gets back up to -20F, it will have some pressure back in it.