The furnace is controlled by an internal circuit board. The thermostat is like an off/on switch and merely starts a sequence to light the heater. Once the blower starts it blows air against a "sail" switch which closes letting the circuit board know the fan is running. The fan will run for a short period to clear any propane then the gas valve will open and the igniter will try to light the furnace. After several tries if the furnace does not light everything stops and you start over by switching the furnace to off then back to on.
It seems unlikely (but maybe possible) that moving the thermostat to 90° is what solves the problem since the thermostat just sends a simple "turn on" signal to the heater circuit board. Possible problems ..
Sail switch not working
Not enough dc voltage to actuate the igniter (low battery)
Gas valve not opening
Circuit board is bad
Not enough propane to light the burner
If you do not hear the igniter "clicking" then either not enough battery voltage, sail switch not working or circuit board is bad.
Apparently the Coleman-Mach thermostat is marginal and frequently replaced with a digital one. Here is a link for that replacement.