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Here's an easy test: Light a stove burner, turn it up to high. Turn up the thermostat to cause the furnace to "come on". As JRTRH stated, the furnace will start with a "clearing" cycle. Now, watch the stove. After this 15 second clearing cycle, the propane will be introduced to the furnace. If the stove burner "goes out", you have propane problem. Check if the tanks are filled, the pigtails are not restricting flow, the regulator is rated for high flow, etc. If the stove burner stays on, then start thinking about the furnace ignitor, sail switch, etc.

DW and I helped an older lady last night with furnace problems when it was 55F in her Everest and 23F outside. Her furnace acted in the same way as the OP. Additionally, her propane detector would flash but not alarm. It was an easy fix - both of her propane tanks were closed - just turn the valves slowly to the left to open the tanks! When we left, the inside of her Everest was at 65F and her propane alarm was "green" (no gas detected). It was the slight about of propane released but not ignited in the furnace that caused her propane alarm to "give a warning".

Ron