MBA Mid-2013 Battery drains to 0% when shut down

I shut down my 2013 MacBook Air (bought in Dec. 2013) after backing up and fully charging the battery, then put it away, as I was not using it. It was shut down, not asleep. This was about a month ago, Today I took it out and it would not start up until I connected it to an outlet, and the battery was at 0%.

Is this really normal, especially for a machine that might routinely be unused for a while (such as someone who buys it for working on business trips)? I don't want to leave it plugged in all the time, yet if I don't, the battery totally drains... and that's not healthy either. I fully expected it to be down to 80% or so, but not 0%... and of course I have no way of knowing exactly how long it took to get that low.

Has anyone else experienced this? How do I work around it?

Thank you for any help you can offer.