This happens to me all the time. Just unplug the mic and plug it back in. If that doesn't work, do it again. If it doesn't work after five times, contact Microsoft for a replacement headset. Edit: to ensure it's working, tap the mic with your finger instead of saying something and look for the green circle to light up.
Kinect launched in 2010 and seven years and two versions later, Microsoft stopped making the gear. A year later and the company stopped offering the accessory for newer Xbox consoles. In 2020
A Kinect sensor bar can get the extra power in either of two ways. The newer, small Xbox 360 consoles have a specially modified USB connection on the back that can provide extra current. Owners of the older, larger Xbox 360s must use the Kinect power supply that is connected between the sensor bar and the console.
As of the evening of Aug. 17, fans have composed the following rough list of games and unique SKUs that are still exclusive to the Xbox 360 Marketplace, which will no longer be legally available
HO0UQ4.