Your furnace rely's totaly on a 12v supply. When it gets around 11v the fan can slow down to the point it no longer activates the sail switch which sends a signal to the gas valve that the fan is blowing and it's safe to fire the burner. Also a low battery will cause issues with the circuit board on your refrigerator in the same way. The only way to correct this is to keep your battery charged, either a generator, solar, or plug in your truck and run for a good while.
Walter and Janie Rogers
2012 Sundance 277RL
TV 2006 Silverado 2500 6.0