On May 16th 2013 Apple released the MacBook Air Flash Storage Firmware Update 1.0. Since I have experienced the described symptoms I really want this update.
However, the Mac App Store will show that I can still update the Firmware (again) after a restart. Since I waited for one minute, as required in the update description, I do not know what's going on.
After three attempts to install the update the Mac App Store still offers to install it once again...
The update description also mentions:
Boot ROM or SMC Version Information: After the update, you will have Revision TPVABBF0.
How can I check latter version information, in case this is a bug in the Mac App Store app only and the firmware update has been installed successfully?