As the others have said, it might be an issue with the cover. Something like this was reported a while ago. The problem turned out to be that the cover had an internal pocket that was touching the screen and prevented the device from sleeping and used lots of battery. Kobo did change things so this should be OK, but it is worthwhile testing what happens if you don't close the cover and let the automatic sleep happen.
Another possibility is the automatic sync. I've seen something like this few times if something goes wrong with the network. The sync doesn't happen but it keeps trying. This chews through the battery and I have had hangs when I start to use the device. Turning the automatic sync or the WiFi off should test if this is the problem.
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