Hi
On the "normal" fridge, it tries to fire the LP multiple times. Once it goes through this sequence, you get the "check" signal. It does not continue to try indefinitely. It is quite possible to get enough air in an un-used LP line that the ignition sequence will time out before the fridge "lights up". Most recommend you fire up the stove for a minute or so after turning on the LP for this reason. Exactly which appliance best purges your system is a "that depends" sort of thing. You may have to experiment a bit.
Second possibility is a failed / dirty igniter on the fridge or a dirty gas orifice. Both will require a bit of digging to check out. It may be as simple as a "cooked bug" in the wrong place
Bob