The "black 15 amp fuse" is probably an "automatic reset fuse" (think mini circuit breaker). Once the amperage rating is exceeded, it opens, and when it cools down, it resets and starts working again. Over time, it weakens and starts opening at lower and lower amperage loads. Once it "weakens to the average furnace amperage load" it starts "becoming unreliable" and the furnace may or may not work normally. It'll always "fail at the worst time" (as you've found out)...
The blue 15 amp fuses (haven't seen green15 amp fuses in years) are a "single use fuse", once they exceed the amperage rating, they melt the thin center section and need to be replaced before the amperage flow can resume, but they always work at the "rated amperage and don't weaken"....
Dometic, in their "great wisdom" elected to recommend a "auto reset fuse" for the furnace electrical supply circuit. You see how "great" that idea really was.....
ADDED: Check your fuse panel closely. If your trailer was previously owned, the fuses "might have been replaced with greater amperage ratings" to solve a blown fuse problem and could be a fire hazard. I believe the fuse panel in your trailer is "rated by WFCO" as 15 amps on all the fuse positions except the bottom two, which are rated at 20 amps.... Normally, 15 amp fuses are blue, 20 amp fuses are red and 30 amp fuses are green. If you have "all green fuses" they may indicate a "previous problem that you need to address"....