Cannot format MacBook Air SSD, stuck at waiting for disks to reappear
It is completely possible that the SSD is toast. It is also possible that Disk Utility just can't fix it. There are other disk repair utilities out there like DiskWarrior, Drive Genius and the like.

If you don't have one, you should. you won't use it often but will be glad you have it when stuff like this happens.

Failing that and assuming that you already have a backup you can boot to the recovery partition and use disk utility to remove the current partition and reformat a new one. Then use internet recovery to re-install the OS.

If Disk Utility won't format/re-partition the SSD then the drive is likely toast and you should make an appointment with an Apple Genius to have it repaired.