The bigger the problem, the easier to overcome.
This is a mechanic deeply rooted into both the minds of the audience and the writers, and thus, is a common and accepted narrative device. As problems and obstacles pile up on a character, there comes a point when the problems can be summed up as a singular problem requiring a singular solution.
For example, if the hero is faced with one enemy, it might be difficult. If two enemies, it might be even harder. If ten... the enemies are no longer individuals, but one group... and one is clearly a smaller number than ten, requiring only some clever trick or strategy to best.
This is the reason why a hero might be crushed by one or two rocks, but will be able to bust out from underneath one pile of rocks.
It is also the reason why the bad guy can defeat the entire police force or army, because it's just that: one police force. One army.
As the entire world turns against the hero and everything imaginable goes bad, suspicions mount in the reader's mind that they have a trick up their sleeve that can bring everything back to normal.
Compare Wake Up, Go to School, Save the World, which suggests that for Kid Heroes defeating the forces of evil is considerably easier than getting their homework done on time and asking people out on dates.
Truth in Television, too: as a person becomes troubled with more and more difficulty, they tend to take a step backward to look at all the problems as a whole and to devise a strategy to deal with them.