I've observed this a few times as well. Following a suggestion from another thread, I noticed that often the Reader does not enter deep sleep mode (standby) correctly when it was booted with a connected charger (for example when booting after a shutdown caused by a fully depleted battery). In this case, the battery depletes within a few hours. You can check whether this is the problem in your case by pressing one of the page-turn buttons when the reader appears to be in standby mode; if the reader wakes up from this button press, it did not enter standby correctly.
The cure is to switch the reader off after removing the charger and to reboot it without any USB cable attached.