What condition is the cover in?
I say this because as they get old and start to fray at the edges, sometimes the little magnet that triggers a sensor for the iPad to turn on and off falls out or moves inside the cover. iFixit has a tear down showing the location of the magnet in an iPad 2 Smart Cover and also the location of the sensor in the iPad itself -
HERE. You could check the operation of the sensor using any old magnet I would have though. Got any fridge magnets?