Firmware Update 1.0 for MacBook Air 2012 Not Installing
Do you happen to have FileVault enabled? If so, you cannot update the firmware on the drive at this state. 

The firmware update happens before the OS decrypts/unlocks the drive, thus at FW update time, the drive is not accessible.

The only solution I know is a bit of a pain: 


turn off FileVault
run the update
turn FileVault back on