Once you boot into internet recovery and you can't see your SSD, you probably have had a SSD failure.
Let me guess... you have a 64gb or 128gb SSD model?
Unfortunately, according to my informal searching here, it seems to be too common for 2012 MBA that have the Toshiba/Sandforce SSD drives to have a premature failure.
See this thread
here where several others also have had SSD failures and so far all have been 2012 64gb/128gb Toshiba/Sandforce drives. Really hope Apple is keeping count of these failures and will do 'goodwill' out of warranty repairs as the failure rate (yes, it's anecdotal) seems to be too high for these drives.