9 out of 10 times the culprit is low voltage. See about plugging into a generator or other AC source for a little bit OR hook up a set of jumper cables to the tow vehicle (running of course) to charge the trailer battery. Try to start the furnace while hooked up to this exterior power source.
As the OP stated, the stove is working. Depending upon the system layout, the furnace may be the farthest appliance from the propane cylinder. Try igniting a few times if the cylinder has been changed recently. My stove is right next to the furnace and it usually takes one or two attempts to get it to light the first time out.
2004 Toyota Tundra SR5 (V8, 4WD, TP, TRD)
2005 Fleetwod Allegance with axle flip
Honeywell 2000i Generator
Me, DW, DS, DD, & Chicken-Dog