I have a 2012 Nexus 7 running KitKat. I have a hunch that it is not charging properly. Specifically, if the system is on and the device is plugged into the USB wall-charger, the battery indicator says "Charging" but there is a slow decrease in charge over time. I have few apps actually running, some checks over Wi-Fi every 5 mins or so (email, feeds), and the device is unused most of the time. It charges to full if switched off and left plugged in.
I obviously need to investigate this more closely, check screen and app power consumption, etc, but before I go on a wild goose chase... is it actually possible for a device to consume more power than it receives via wall-charging?