Janet, in the propane furnace, there is a "stack" of sorts from where the actual flame is leading to the outside of the unit. This stack can be blocked by debris or spider webs. Spiders apparently like the smell of propane and will inhabit the stacks.
Also, it's possible that the igniter is having problems. If the thermocouple is bad or slightly out of adjustment, the flame won't stay lit for very long. You will get the initial ignition ("whooosh" sound followed by running noises) and then it stops.
There is a blower in the furnace that comes on before ignition that clears out any stray fumes. If that blower is not coming on, the furnace won't run.
You said there is a red light flashing on the furnace. If you have the manual, maybe you can look up what that means. If not, give us the make and model and I'll see if I can find the manual online.
One other possibility comes to my mind. If you run a tank completely out and then switch to the other tank manually, there will be some dead space in the propane lines from the tanks to the appliances. It will take a few cycles to get the lines fully full of propane again.
If that is the case, what I do in my trailer is to light up a burner or two on the stove. From what I can figure, the stove is almost on the end of the line so if a burner will stay lit, that pretty much means the rest of the propane piping is once again full of propane. Even then, the fridge and WH and furnace may need to go through a few lighting cycles before they will light reliably once again.
Let us know how it goes.
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