If, as you say, the connection feels loose, maybe the micro-USB connector had been forced sideways by the cable and lifted up the printed circuit board pads where it was soldered. My daughter, running while playing, entangled her leg in my Kindle cable while it was charging and the same happened to my connector...
in this case, you will have to take your Kindlle to a repair technician and have the connector re-soldered to its printed circuit tracks, repairing them in case they are broken.
The following guide can help the person that is going to open your Kindle to repair it:http://www.ifixit.com/Teardown/Kindle+Fire+Teardown/7099And if you search in YouTube for 'Kindle Fire USB charging problem', you will find that there are more than a thousand videos showing how to repair the power and signal connections.
Hope you may find this info helpful!
Miguel L. Martins