I assume by "cover" you mean the Smartcover (or something similar) which is supposed to put the iPad to sleep when closed. When I close my Smartcover, it makes a clicking sound that lets me know it has gone to sleep. You can also tell by lifting the corner of the cover slowly and looking to see if the screen is off before coming on (there is a half second delay when the cover is opened). Finally, you may want to check the Settings to make sure the Smartcover sleep mode is on. Whether the cover is working to put it to sleep or not, if you're not actively using it, it should fall asleep on its own after some time.
All that aside, I would be concerned about the fact that it is draining "really fast." Heck, even if your iPad for some reason doesn't sleep under any circumstances, it shouldn't be draining "really fast" if not being actively used. I never shut mine down completely. Even at night, I just close my cover and let it sleep overnight. When I wake up the next morning, it usually drops 1 or 2% at most, due to the notifcations, alarms, etc.