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It does sound like a bad battery. It's been twenty days since my last charge and my battery is at 40% after 35 hours reading, that's with turning it off after I've finished reading for the day and wifi off. My battery does appear to deplete much quicker from 100% to approximately 70%, my girlfriends is similar, that happens with these sort of batteries.
As Mrs Often wrote, charging it twice per week is unacceptable and you should return your device.
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