As you seem to know, the orange light indicates a charging status.
If things shut down when you remove the power supply, you may have a battery that isn't taking a charge.
Do you display the battery status in you Apple menu bar?
To display it go: AppleLogo/System preferences/Energy Saver, then, check the box to "Show battery status in menu bar".
Once the display is present, click on it to get its menu, goto, Show/Percentages
At full charge, I get anywhere from 97% to 100% displayed. And a green LED at the mag connector.
Do you use the Air on battery a lot? Because every battery has a recycling limit/life.
I don't know the exact figure, but for an example say, 1000 charge cycles.
That would translate into say one cycle per day, a little over a three year life expectancy for the battery.
How long have you had that battery and how often do you use the battery?
Let us know results.