I'll elaborate a bit;
A propane tank is filled with liquid propane that will stay a liquid in an open container at -45°F. At normal room temperature, it has to be enclosed to prevent it boiling off. The pressure inside the tank is going to be the vapor pressure of propane at the outside temperature. For 70°F that will make the tank pressure be around 100 PSIG. This pressure will only increase if the tank gets warmer, and decrease only if the tank gets cooler or is empty. The internal pressure will not drop any until the tank is empty during use, as long as the tank doesn't freeze up. There-in lies the problem with using a 20 pound tank. As the propane boils off, the endothermic transformation makes the temperature drop. This in turn lowers the vapor pressure. Once it reaches the point where the outside air pressure is the same as the inside vapor pressure, the propane stops boiling and no gas will be delivered.
So the answer is - The pressure will remain the same until the tank is empty or freezes up.
BTW, The above information explains why a propane tank explosion is a very rare event. The tank will have to be exposed to sevre heat before the pressure can reach the bursting strength of the steel tank.
Even in a fire, all the Fire Dept. needs to do is train a hose on the tank to keep the skin temperature low enough to keep the tank pressure below a couple hundred pounds. If the tank valve breaks, and the propane starts burning, then there is almost no change of an explosion, because the tank pressure will remain fairly constant as the propane boils off and creates the flame. If the break is in a larger diameter pipe, and the propane flow is high, the tank will cool itself so low that the flame will barely burn.