tl:dr The writers didn't want the engine to fry and stop working altogether.
Unfortunately, for you to get a logical answer to this question, there has to be an actual design that works in the real world, for that Pod Racer. I realize that is not what you wanted to hear, since you want a Canon Answer based on the mechanics involved with the workings of Anakin's Pod Racer.
The reason for Anakin's troubles throughout the race, is "Drama". His problems, and the way he overcomes his problems, are Plot Devices. Anakin did not race this amazing Pod, while trying to keep it from blowing up or flying apart every passing moment. He most certainly did not. It never happened.
What happened is this. The writers sat down and wrote a story about a character named Anakin who was in a fictional Pod Race. They described how the pod would look... or maybe the appearance of the pod was designed before the specifics of the race were worked out. In any case, a fictional character was detailed in some specific events that created drama and left the viewer with the impression that this simple, young, male character was anything but simple.
Since the actual workings of the Pod Racer are fictional, and no one knows how they actually work since they don't exist in real life... the writers can create any kind of situation they like... from cables flying off that obviously shouldn't fly off... to parts getting damaged that obviously are necessary but don't seem to do anything after they get damaged... to engines that should explode or cease working but don't. They can create any kind of situation they want and the audience can't argue and say "Oh, that doesn't work that way." because the Suspension of Disbelief is already turned on. This is a universe where crystals power light sabers and the planet-killing lasers on moon sized space stations. The writers get to say whatever they want, and they don't have to explain why it works that way.
I could say that the character of Anakin Skywalker didn't want the fire to spread, so he subconsciously controlled the fire with the Force. The Force was pretty much the reason for everything else in that race. The magnetic handle that managed to grab only the end of the cable to get it in place? The Force did it. His uncanny racing skills for someone so young? The Force did that too.
I could say that each engine was designed with multiple fail-safe devices to keep a fire from spreading... but I'm still wondering about what Repulsorcraft use for fuel in the Star Wars universe. It might be Rhydonium... but we don't know that for sure. We do know that the "mechanism" behind the Pod Racers, is http://starwars.wikia.com/wiki/Repulsorlift, and that the Pod Racers themselves don't appear to have any fuel tanks to speak of. So... the reason why the fire didn't spread, could be because the fuel used to power the Pod Racer wasn't actually combustible by fire. If the Pod Racers are powered by Khyber crystals, for example... there's no fuel to spread a fire in the engine.