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Have you tried turning off your wifi to see if that is draining your battery? Also try changing out your power cord.
You an also try holding the power button for at least 20 seconds, ignoring the question of whether you want to shut it off, and allow the KF to reboot. That sometimes solves the issue of not charging all the way or loosing it's charge. But I would also try another power cord and if that doesn't work try turning off wifi when you don't need it and see if that will hold the charge better. If that doesn't work then it sounds like your Kindle Fire is defective. You should still be under warranty so all you have to do is call them and they will send you out a free shipping label to send kindle back.
You can also plug in the charger that came with the KF and turn the KF off. "Turning it off" means holding the power button until the message appears asking if you want to turn it off. Say yes. (Note: Use the Amazon cable unless you are ABSOLUTELY SURE that the cable you're using supplies at least the same amperage as that cable, about 2 amps. Do NOT use cables that charge more slowly. They won't hurt your battery but they may well throw off the synchronization with the battery monitor.Let the KF charge for at least four hours, preferably overnight. Pay no attention to the orange or green light. Don't turn on the KF to check on progress.Unplug the KF and boot it. Use it normally until you see the 15% battery remaining warning. At that point, shut it down again. Do NOT allow the battery to discharge completely. It probably won't hurt the KF or the battery but it does shorten the battery life if done repeatedly. (The software should shut down the device with about 5% charge remaining but why take a chance.)Repeat the charging process above.Once you've cycled the battery charge/discharge process twice, you should have a good discharge profile. From then on charge the battery on a regular basis even if you have not reached the 15% remaining level. Don't worry about "overcharging." The KF will not allow itself to be overcharged unless it's faulty. And if that happens, you'll be able to tell because it will be HOT when you take it off the charger. Just charge every night or whenever you reach the 15% charge remaining warning.If you never reach the 15% charge level during normal use, do so purposely about once a month and charge completely to 100%. This should keep your battery profile in sync.
You can also try turning down the brightness on your KF, that eats up a lot of battery.