Why does my MacBook die everytime I unplug it from the charge cord, when I still have 36% battery life?

My MacBook is only a few months old and I've taken great care of it. But yesterday when I disconnected the charge cord, the screen went black and would not restart until I reconnected the cord. I've never let the battery fully drain (didn't think you were supposed to), but I also try to not to leave it on the charge cord constantly.

Any help or suggestions as to what to do would be appreciated!