I don't think the furnace fuse or the furnace sail switch could cause that problem. The fan would not run at all if the furnace fuse was blown, and the sail switch prevents ignition of the gas burner but doesn't ever shut off the fan.
15 seconds of fan time sounds like the burner chamber purge cycle. The fan runs for about 15 seconds to clear fumes from the burner before starting the ignition cycle. Maybe your furnace ignition board isn't taking the next step after the purge cycle? Still seems odd, though, because the fan should continue to run as long as the thermostat is calling for heat. Even if the burner never lights. My other thought is that the thermostat (or the zone controller on a multi-zone system) is not keeping the "heat needed" signal line active. It's a +12v signal to the furnace and the furnace is supposed to run as long as it is present, and stop 15-20 seconds after the signal disappears.
Former owner of 2004 American Tradition and several other RVs
Home is in the Ocala Nat'l Forest near Ocala, FL
Summers in Black Mountain, NC