Leaving wifi on is a huge battery drain, syncing every night makes the drain even worse.
I've always had sleep covers on mine and I've had zero problems with any battery drain. I also never shut the light off, I let the sleep cover shut it off so it comes back on as soon as I open the cover to read again.
If your sleep cover isn't working and leaving the light on, it's easy enough to see, just go into a dark room or closet and look at the edges of the cover. Or when you open it, you'll always see the light off and then turning on as another way to check it.
I'd bet anything it's leaving the wifi on and nightly syncing though and not a problem with the sleep cover.
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