I had this problem as well. I tried updating the firmware, and resetting the kobo twice. I did different recharges (two full recharges after completely dying, several partial recharges)
No luck, so after two weeks of owning the Kobo Wireless, I decided to just exchange it. I went to Indigo (Eatons Center), and the staff there were friendly and gave me an exchange.
Whats the correct behaviour of the Kobo? After a few hours, is it supposed to power off? I noticed that with my newly exchanged one.
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