It sounds like you covered the usual bases - cover, wifi, indexing. The only other things I can think of is temperature - either too heat or cold - and a few reports that topaz books can get stuck and/or don't show that they're indexing.
I can read for 12 hours straight on my K3 3G+wifi at medium font and only lose 1/4 to half my battery.
If it were me, and I knew temperature wasn't an issue, I would try these fixes, in order from least to most desperate:
- A full reboot
- Allow it to run down as far as I could, then charge it overnight - or at least 8 hours
- Delete any topaz books
- Delete indexes
- Do a reset to factory conditions
If none of those worked, I'd call and have them send me a new one.
Good luck.
