Most likely a vaporization issue especially for a 20-lb bottles of propane. As the tanks empty the available BTU's reduce as the vaporization of propane cools the liquid (same process that makes your AC work). This gets worse as the temperature drops as the tank can't use the outside air to heat the propane. As the tank gets lower and the temperature outside gets cooler the colder the liquid propane gets and can even freeze.
There's a better explanation here:
Propane Vaporization that will show you how many BTU's are available and how it all works. Scroll down to "Vaporization Rates of Cylinders"
What probably happened is you drained that tank down enough to where it was not supplying enough BTU's to light or sustain the furnace but not enough for the changeover to sense an empty tank. Especially if you were hitting the furnace hard in cold weather on an almost empty 20-lb tank. You can see where the level of propane in the tank is by looking at the frost line. Where the frost forms is about the level of the propane in the tank.
So best option is to keep those tanks full or upgrade to 30-40 lb tanks if you can use it. Not sure about an oil pan heater but some will bathe the tanks in warm or hot water to help keep the flow up.