I have a Kindle DX that has twice discharged the battery completely over night when the device was laid flat on a table. Normally I put the device on a shelf standing upright when it isn't in use and the battery never discharges in that case.
It isn't a case of leaving the device "on" because the DX turns itself off after a few minutes, and I don't think that on/off affects the rate of discharge. The DX is an e-paper device that, as I understand it, consumes power only when the pages are written to the screen.
Is it conceivable that the position of a Li battery could affect its self discharge rate?