Microsoft did a recent interview with PC Mag. The shut down for the xbox 360 is anywhere from September 30th 2016 to November 30th 2016.
I have noticed since last March, any free 24-48 hour xbox live codes given away with 360 games expire in September 1st 2016. No recent codes given with 360 titles are usable past November 2016. Microsoft did the same thing with Original Xbox title's codes. Same pattern of behavior. So it fits. The 360 is losing live support fall/winter of next year.