MBA won't start without plug

My Macbook Air that I absolutely love (besides this issue) won't start after its auto powered down without being plugged into a wall, even if its battery is fully powered.
I brought it to school the other day and forgot the power cord in my backpack and I couldn't get it to power on so it was useless all day and I was unable to get at my notes. So freaking frustrating.

Is this normal or do I have a defective machine?

No, this isn't normal. Your MBA should start up from a charged battery the same as it does when powered from the AC mains. If that continues you may wish to take it on in to Apple and have it looked at. The trouble could be with the DC input power board or perhaps something else.

Regards.