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This issue can be faulty software, a faulty battery or a faulty charger. The easiest and quickest possiblity to rule out is software.
So lets try this master reset first and let me know if this solves the issue or not.
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My apologies for the delay in getting back to you.. When you replied a day later I was away for the holidays.
I wont be online much today, I had a few moments and wanted to catch up on replies.
Youre best bet at this point would be to replace the charging cord and battery. You can get a new charging cord here for 35 cents plus shipping
And for 25$ you can get a kit here http://amzn.to/1mDP9LK
That kit includes a new battery, the tools you need to replace it and a video that shows you how to replace the battery.
With a new battery and charging cord, the device shouldnt have any issues staying on and working normally.
If you have any further questions let me know, and Merry Christmas!