MacBook Air shuts down unexpectedly

First you should get an app that can help you see the battery condition. 

As to why your MacBook Air is shutting down is often a messed up SMC. What happens it the SMC holds a high and low watermark (the batteries charge) so it can go into power save mode so you don't loose what you are working on. I would reset it following this Apple T/N:

Reset the SMC of your Mac - Apple Support

Then after your system is fully charged let it fully discharge at least two times this will reset the low water mark to be at the correct level.

It could either be that your battery is low on charge. Charge it, and try it again once it's charged. If you suspect problems with your battery (such as quick energy drain and/or persisting automatic shutdowns, etc.), change some settings or bring it to a repair shop professional.