You will probably find that a bunch of physical servers are networked together to create a larger one, within that heaps of virtual servers, within that the back end for a game. They only need to close down the virtual server for Halo 3 and replace it with a newer one for a new game.
It is upto Microsoft to manage the server
There is no real need for the back-end to stay online as most people are spending most of their time playing a newer game, the majority will not notice it gone.