I did a similar project with Kindle Paperwhite running for over 2 months on a full charge. It would boot early each morning, connect to wifi, pull latest weather and news, generate a png containing weather and news, show the png on the screen, shut down wifi, set RTC to boot again tomorrow and power down.

The problem I had is that eventually when it ran out of battery, I charged it and the process didn't kick off again. Probably I just need to ssh back in a get it going again, but I lost interest at that point!