You should always use the charger that came with the Nexus and use AC power, especially if the battery is low. I don't understand why people insist on charging via USB. It's slow and the tablet wasn't really meant to be charged that way, that's why it comes with an AC charger.
Also, don't ever let the battery drain to the point that it shuts off. When it warns you the battery is low and tells you to connect the charger, connect it. I personally don't let any of my devices get below 15% and I've had zero battery/charging problems.
Galaxy Tab 3 8.0
Galaxy Tab 2 7.0
Dell Latitude 10 (Windows 8)