For the record, adding my story (also told in pictures on my blog):
Mid-2012 MBA bought in Berlin on September 22, 2012, died in Tokyo on September 28, 2013, in the same way as described by other posters.
Went to Apple Store Shibuya, where a genius ran tests on it for half an hour. He concluded SSD failure (Toshiba 128 GB) and offered to replace it free of charge despite the warranty had just ran out and it was bought in Germany. It would take 2 weeks and they would keep the old SSD.
I couldn't wait that long, and I also didn't like the idea of Apple keeping my old drive, so I had to decline his offer. Instead I went to Akihabara to search for a new SSD. It wasn't easy with the air's special connectors, but I finally found a OWC 240 GB (smallest size available) for 37,000 yen ≈ 275 euro ≈ 377 usd. Installed it myself and everything works fine since then.
Some notes:
I had done some update shortly before this death happened, but I can't remember exactly what it was.
I had very little space left on the drive.
I used FileVault.
Some posters mention that the part of the Toshiba SSD that failed was the Sandforce controller. Now I just checked my new OWC SSD. It also uses Sandforce. Does this mean I can expect another year before next death? Or am I safe as long as no firmware update? (Though I guess no new firmware will be pushed to a third-party part.) Would it be stupid to update to Maverick? (I definitely won't do it until I'm back in Europe and have made tons of backups at least.)
I've contacted Apple regarding a refund, since they write:
"If you believe you have paid for a repair or replacement due to this issue, contact Apple regarding a refund."
Yes, I think I "paid for a replacement due to this issue" when I bought the new SSD, but no, I will not get a refund according to the German support. (I think I might actually try with the Japanese support too, you never know.)
As a last note: When death happened I tried to boot in terminal mode and doing so I could actually browse the folders and delete files using unix commands. This bogged the Genius at Apple Store too, since it implied the SSD wasn't totally dead. But maybe this is because of that Sandforce thing. The actual data might be undamaged, but the way to get to them is f-cked.
Oh, and even though I think it's good that Apple has done a recall, keeping our computers for 2 weeks is unrealistic. Since they know about the problem, they should stock up with replacement SSD's in all stores and exchange them while the poor customer is waiting, or overnight at worst. Why can a tiny electronics store in Akihabara stock these items, but not Apple themselves?