Reference

The battery does not charge.

    Make sure you have securely connected the tablet with the USB cable for Multi Port, the USB cable for Multi Port with the AC adapter, the AC adapter with the AC power cord (mains lead), and the AC power cord (mains lead) with an AC outlet (wall socket).
    If the temperature of the tablet rises in situations such as while using apps ([Browser], [Email], [Camera], or playing videos/music), the battery may not be charged. If the temperature rises, shut down the running apps. The battery will begin to charge when the tablet returns to normal temperature.
    Your tablet does not support charging the battery via USB connection from a computer or a commercially available charger not designated by Sony.