I have exactly the same problem as many others. The SSD crashed on November 6, I took my MBA to an Apple Store in Orlando, FL, where the SSD failure was confirmed. I received the same story that due to the shortage of the part, it could be a month before I receive the machine back.
A few years ago, I switched both my personal and business use to Apple products for several reasons, one of which being the lack of reliability of the Windows computers I had purchased previously. My faith in Apple is now severely shaken. The company is attempting to do the right thing by replacing the part, but asking individuals to go without the affected computer for any more than a week, in my opinion, is completely unreasonable. I am willing to pay more for a better product, but expect to receive a machine that functions or is fixed within a reasonable amount of time. Apple is not doing enough in this situation- if they cannot fix the issue within a week, they should be offering us NEW 2013 MBA's (not refurbished 2012's) or simply expecting that we can wait a month to receive a repaired computer.
When it comes time to make my next purchase, I will be giving serious thought to whether or not I will be purchasing Apple computers.