Hi,
What colour is the charging lamp when it stops charging, green or orange? Have you tried letting the battery run down to a low value (say 15-20%) and then seeing how far it charges up to?
If that doesn't change anything have you tried ''resetting'' your Chromebook?
Here is a link to the user guide, scroll to p.58-59 to see how to reset your device.
http://dlcdnet.asus.com/pub/ASUS/EeeBook/C201PA/0409_E10040_C201PA_A.pdf