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All games will come to an end eventually, but I have a feeling that Halo 3 still have a good couple years, maybe even a good decade, before they shut it down.
It's going to be similar to the Xbox / Xbox 360 transition:
When the newer Xbox comes out (supposedly called the Xbox Spectrum), they'll give some time for the 360 users to transition, which may be 3 or 4 years. Then after that they'll either shut down the old 360 game servers OR hopefully they will be smart and keep the games online and playable on the Spectrum.