Q: iphone 4 with ios 6 update do not disturb isnt working

Perform a Reset... Try again...

Reset  ( No Data will be Lost )

Press and hold the Sleep/Wake button and the Home button at the same time for at least ten seconds, until the Apple logo appears. Release the Buttons.

http://support.apple.com/kb/ht1430

You use the Do Not Disturb setting while your iOS device is locked...

From Here  >  http://support.apple.com/kb/HT5463