This took me a while to read because I ended up going down the rabbit hole of reading about the PoqetPC - a tiny subnotebook that could last for weeks or months on two AAs: http://www.bmason.com/PoqetPC/
I had a Fujitsu Lifebook P-2046 in college (2002-2007). It was frustratingly slow, but could manage 15 hours of battery life. Even five years after purchasing it, people would remark on how compact it is.
I had not one, but two given to me by a family friend in the mid ninties! I was young and it was epic. I could send faxes via a 14.4k serial modem with a PoqetPC to parallel, parallel to serial adaptor. I could play stunts on it, and write BASIC programs, what more would you want at age 7? Yes the battery lasted weeks, and the memory cards held a small watch battery in them. I've still got one somewhere, which I now want to dig out.
I would pay lots for a modern thing with that form factor.
The Pandora [1] is a few years old at this point. I had one for a short while and wasn't too impressed. There will be an update called the Pyra [2] coming later this year.