Battery drains while shut down?

Question

If, having SHUT DOWN (not sleep) my MBA, and let it charge until the magsafe light is green and let it charge overnight, I unhook the magsafe while keeping the MBA off and closed, I leave it TURNED OFF for an entire day, go out to use it elsewhere and when I get there, the battery is completely dead.
Why? What can I do to fix it?
The Air seems to shut down MUCH quicker than my old MacBook Pro, so I don't know if it's just not shutting down properly or not. The same thing happens if I hold the power button for a hard shutdown until it shuts off and repeat the charge/wait process.
Like I said, this is with it SHUT OFF and not in sleep mode. If I can't leave it turned off while I wait in an airport, what's the point exactly? Is anyone else experiencing this? (I know at least one person is on another forum, but no one gave him any answers)

Answer 1

Used the timer on my iPhone. From green status light (turned off) to when I woke up it was eight hours, 41 minutes, 48.6 seconds later and the battery status was as follows:
Model Information:
Serial Number: SMP-ASMB017-3887-8cb
Manufacturer: SMP
Device name: ASMB017
Pack Lot Code: 0000
PCB Lot Code: 0000
Firmware Version: 0009
Hardware Revision: 0401
Cell Revision: 0100
Charge Information:
Charge remaining (mAh): 2938
Fully charged: No
Charging: No
Full charge capacity (mAh): 4977
Health Information:
Cycle count: 9
Condition: Good
Battery Installed: Yes
Amperage (mA): -1101
Voltage (mV): 7522
System Power Settings:
AC Power:
System Sleep Timer (Minutes): 0
Disk Sleep Timer (Minutes): 10
Display Sleep Timer (Minutes): 20
Automatic Restart On Power Loss: No
Wake On AC Change: No
Wake On Clamshell Open: Yes
Display Sleep Uses Dim: Yes
Battery Power:
System Sleep Timer (Minutes): 5
Disk Sleep Timer (Minutes): 10
Display Sleep Timer (Minutes): 1
Wake On AC Change: No
Wake On Clamshell Open: Yes
Display Sleep Uses Dim: Yes
Reduce Brightness: Yes
Hardware Configuration:
UPS Installed: No
AC Charger Information:
Connected: No
Charging: No
That's a 41% DRAIN in battery overnight, with it being turned off.
*Makes appointment at Genius Bar* I'll post results of the visit here just in case anyone else has this problem.