MBA doesn't see SSD. How do I recover my files?
More than likely the files ARE recoverable but the difficulty &amp; cost to do so could either be a little or a lot.  My first step would be to start a case with Apple, either by calling AppleCare (1-800-APL-CARE), visiting an Apple Retail Store’s Genius Bar (be sure to make an appointment beforehand) or an Apple Authorized Service Provider (AASP).  This link can help you find an Apple Store or AASP in your area.  

With the age of your Mac and the issue you describe it might be tied to the MacBook Air SSD REP that Apple announced a few months ago.  Once they evaluate the issue, which will likely be fairly quick since it's possibly a known issue, they can provide you with info on repairing the Mac and recovering the data.  Apple’s policies prevent their staff from assisting (aside from recommendations) with data recovery but AASPs may be able to provide onsite data recovery or more budget friendly recommendations.

The only other thing you might attempt on your own before seeking data recovery from a specialist is to try and browse your Mac from another Mac.  You can do this by using Target Disk Mode, which is triggered by holding T while powering on your MacBook Air. Once it’s in Target Disk Mode you can connect it to another Mac using a Firewire (with Thunderbolt adapter for your Mac) or Thunderbolt cable.  A functioning drive would then show up in the secondary Mac’s OS as an external hard drive.

Beyond that your best bet is consulting your local AASP and/or AppleStore for data recovery recommendations.