This happened to my Paperwhite as well! Discharges (quickly) while plugged in. For me, it happens when it's plugged into a very low-power source, such as a multi-charger with other devices also charging. I'm able to overcome the problem by plugging it directly into the power brick with a dedicated cable. It feels like it needs 5W if power (I'm guessing) to charge, or else it discharges.
It's not a problem with the battery, because once it's charged the battery life is normal.