The "switch" is triggered with a magnet which is in the side of the case.
Try taking your smart cover off of the iPad and just rub the right hand edge of the case up and down the right hand side of the iPad. It should turn off and on as the magnet moves across the switch. You should also be able to feel the magnet "catch" at the right spot.
If this does not work, and you are absolutely sure you have Settings > iPad Cover Lock / Unlock set to ON, it could be a hardware issue. Make sure you try it again after a full reboot of the device (turn it fully off and back on again, not using sleep mode). If it is a software glitch, that may shift it.
Also, just to check, you have a genuine Apple SmartCover? Other 3rd party ones, especially if they are made for the iPad2, can have problems with the magnet being round the wrong way and therefore having the incorrect polarity.
Let us know how you get on.