Hello, My name is ***** ***** I'll be assisting you. I'm sorry you're having problems.
The problem you're having is often due to the software in the Kindle locking up and it needing to be rebooted. To do this, simply press and hold the power button on the Kindle for 40 FULL seconds, then release and wait a full minute for it to reboot (do no press anything else within that minute). If this does not cure the issue, try that reset up to THREE TIMES and wait the full minute to see if it reboots.
If you're still running into problems, then try plugging the Kindle into the charger for 15 minutes, then eject it and try the reboot a couple of more times.
Those are the only steps on a user level you can try to correct this issue, and if it goes beyond that this does indicate a premature hardware fault with the Kindle unfortunately, and in that case, you would need to contact Amazon to have the device replaced under their one year warranty.
If you need further assistance let me know. Before you go, PLEASE DO click at least a 3 STAR RATING, at the top of your screen. That is how I am credited for my efforts by the site. You can follow up any time as needed at no additional cost.
Are you able to get the Kindle to stay powered up?