Burning time does not reapply to entities that are set on fire while burning

To reproduce, set a mob on fire and immediately put out the fire. Notice it burns for a certain amount of time. Do the same thing, but set the mob on fire again about 3 seconds later and put out that fire. The mob won't burn longer no matter how many times it's subsequently set on fire. This problem applies to players as well, but is more difficult to reproduce due to MC-178252.