For low light reciprocity failure, there isn't something magical about a long exposure that somehow affects the film in a mysterious way. What happens is that the light hitting the film has so little energy/intensity that the film doesn't respond as strongly to it - there is a threshold light intensity at the film plane. Below that threshold, the film responds much less to light than would otherwise be predicted from extrapolating the straight line portion of the film's curve. So with light at the film plane at these low levels, exposing the film, for example, for twice as long gives you a result that is actually twice a lesser result than what one would otherwise expect.
The benefit of understanding this is that it encourages people to consider another solution - increasing the intensity of the light reaching the film.
As Vaughn says, a similar thing happens with very high intensity light that would otherwise necessitate very short exposures - the response isn't linear there either.
Although as I understand it there are additional effects one must take into account for very, very short exposures - my memory of the physics involved is a bit hazy though.