The Meaning of Life, the Universe, and Everything.
What's with the becon question? that seems unrelated. To the topic at hand, mob spawners are intended to stop spawning after a number of mobs have spawned. This is limited to a range, and once one mob leaves the range, more will spawn. I know neither the range nor max number, but the wiki says four. I can only assume that this is one of the many differances between xbox and PC, and one of my main complaints when it comes to games that share platforms.