do I need to change the battery'

letting your battery deplete its charge is ruinous on the lithium battery cells.

Dont ever do that if possible, it causes premature battery death.

Considerations for the long life of your Macbook Air. Handling and environmental care tips

Reset SMC. http://support.apple.com/kb/HT3964

Choose the method for:

"Resetting SMC on portables with a battery you should not remove on your own".

If this does not help, contact Apple.

Genius Bar reservation

http://www.apple.com/retail/geniusbar/