LP fireplace: My pilot and burner both shut down
A 100lb tank? In Winter? In Maine? You are almost certainly overdrawing the tank.
Liquified Propane has to boil to provide you with gas, and it takes heat to do that. The pressure in a propane tank is a direct reflection of the temperature of the propane tank, and they will cool to well below ambient temperatures when boiling hard to meet a high gas demand. Perhaps you've seen frost on a propane tank in the summer at a barbecue? Same idea, but in winter tank temperature can fall low enough that there is inadequate pressure in the tank to supply gas. Figure frost in summer is 50 degrees °F below air temperature, reset the ambient temperature to 10 or 20 °F and the tank is down into the -30 °F and below area where there's very little (or no) pressure.
You need a larger tank, and if trying to use it for winter heat in Maine, a larger buried tank is the best bet, since a buried tank is considerably warmer in winter than an aboveground tank. But simply larger will work, if it's large enough.
There is also a reduction in available BTU/Hr vaporization rate as the fill level in the tank drops (on top of the drop in rate with ambient temperature) so it's possible that it may work better if it's filled more, but a larger tank is the surer cure.