My kindle fire hdx 7 running lollipop 5.1 is charging but not keeping the power

Try a different battery charger.
Maybe you are using a battery charger of a phone.
They have the same plug but different Amperage.
Usually tablets have more powerful battery charger than phones (2.1A instead of 0.5/1A).

The battery charger that you are currently using seems to have enough power just to keep your tablet alive, but not enough to charge it.

You can check on the data written on the battery charger's body the maximum amperage.

James, You have to make sure the Kindle is charged, try holding the button longer, maybe even up to a minute, hopefully that will do it. Check the attached links,instruction and guides, Good luck
"I hope this helped you out, if so let me know by pressing the helpful button. Check out some of my other posts if you need more tips and info." You can also do a search on google for this issue, seems there is a lot of info. on this problem.
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Put it in airplane mode and charge, turn off to charge, close all windows and apps. Try new charger, clean port and plug with alcohol. If none of those work check warranty

1) Plug it into a different USB port on your pc;
2) Use a different USB charger - look to see if the one supplied with your 'phone has the common Micro USB jack;

Fire's take about 14-16 hours to charge from a pc and 3-5 from the wall,

Her is a possible solution:
1. Plug into the original charger, hold the power down for a full 30 seconds, release. Let charge in this state for 12 hours.
2. Lease the device plugged into the charger, while you have the device plugged into power, press the power button for a full 40 seconds, release. Wait for 5 seconds and then press and release the power button. Did the device wake up? No, continue to step 3.
3. Plug the device into another charger, if you do not have an charger from another phone go to Staples or Radio Shack pick up a new Kindle or Universal charger, make sure you can return the charger.
4. Plug the Kindle into the new or alternate charger. Hold down the power button for 30 seconds release. Let charge for 12 full hours.
5. Unplug the Kindle from the charger.
6. Press the power button for 40 seconds - time it. Release the power button, wait for 5 seconds, then press and release the power button. The Kindle should wake up. If not, proceed to step 7.
7. If you can not wake up the Kindle from a 'hard reset' the Contact Amazon directly for a replacement.

The Kindle Fire will not turn on, correct? Let's try a hard reset.
Step 1: Unplug the device from the charger
Step 2: Press and hold the power button for 30 seconds
Step 3: Release the power button, then press and release the power button normally, the Kindle should wake up
Step 4: If the Kindle does not wake up, find an alternate charger or go down to Radio Shack or Staples and get a new charger
Step 5: Plug in the new Charger to the Kindle for 12 hours when done leave the Kindle plugged into the charger
Step 6: While the Kindle is plugged into the charger, press and hold the power button for 30 seconds. Let the Kindle charge for another hour.
Step 7: Pickup the Kindle, press and release the power button normally, the Kindle should now wake up.
Step 8: If the Kindle does not respond, contact Amazon for a replacememnt

Let's try to reset the charger system.
Step 1: Unplug from the charger, press and hold the Power button for 30 seconds
Step 2: Plug into the charger. Press and hold the power button for 30 seconds
Step 3: Let charge for 12 hours
Step 4: Unplug form the Charger, run the Kindle until totally dead.
Step 5: When DEAD. Press and hold the power button for 60 seconds.
Step 6: Plug into the charger, let charge normally
If this does not reset the charging system you have either a faulty Kindle or a faulty charger, contact Amazon for replacement.

This is usually a sign of either a failing charger or Kindle, let's try to hard reset the Kindle.
Step 1: Press and hold the power button for 60 seconds
Step 2: Plug the Kindle into the changer, press and hold the power for 30 seconds
Step 3: Let charge for 12 hours
Step 4: Turn on and use the Kindle, if it shuts down before 6 to 8 hours of use, contact Amazon for a replacement.