The battery icon the Kindle fire HD is small and gives no indication of usage left, this app allows a battery icon in the notification bar which when you tap it gives time left surfing, reading, music etc and the battery % its a very good app
I'm currently using the free version but seriously considering the paid one.
This app showed the battery was going down significantly over 12 hours with the lid closed. It seems my facebook app was waking up my Kindle all the time so I disabled facebook notifications. This app showed the battery was more or less constant for the following 14 hours afterwards.
Yes, it is complicated but for troubleshooting apps it's the tool you need.