Understanding the Side Switch > http://support.apple.com/kb/HT4085
Close All Open Apps... 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.
My iPad 2 had this problem too. Two days ago the side switch just stopped working out of the blue. I changed it from rotation to mute and back again; I reset my iPad by holding the Sleep/Wake and Home buttons; I even did a full restore to iOS 7.1. The side switch still didn't work.
Then I banged it gently against my desk, back side down. That worked.