From ~500 AD to today, why hasn't anyone occupying Rome actually rebuilt or used it?
Has it been unused since?
Since the sixth century, the Colosseum has housed apartments, shops, hospitals, castles, and palaces - all while serving as Medieval and Renaissance Rome's greatest quarry.
The last recorded event in the Colosseum was an animal hunt staged in 523 CE. Early medieval Rome was distant from the centers of political power, and its most powerful officials - the Byzantine exarch and the pope - had neither motive nor opportunity to stage expensive entertainments for Rome's shrunken population.
Parts of the building were soon re-purposed as shops; the arena may have even become a sort of shopping plaza. By at least the ninth century, people had begun to live in houses built beneath the arches and over the old seating. For much of the twelfth and thirteenth centuries, two noble families struggled for ownership of the densely-inhabited ruins, which were now fortified and crowned by a small palace.
Throughout this period, the Colosseum served as a quarry. Even before the last beast hunt staged on the arena, building materials were already being removed - first the lead and iron, and then the fine travertine (which was burned to make lime for mortar). The process was accelerated by a series of earthquakes, which loosened and tumbled the great blocks of the perimeter and radial walls. The worst destruction took place between 1347 (when an exceptionally severe earthquake destroyed most of the southern side) and the late seventeenth century (when Rome's Baroque building boom slowed).
For more detail on the Medieval Colosseum, I refer you to this excellent page. You might also be interested in my Colosseum page, though this is concerned exclusively with the classical building.