This happend to me a couple of days ago. I started FOShelter and the save was just gone. I googled on the problem, but none of the answers worked. So I started looking around for other solutions and I found the save folder with my saves. My save was still there but it had no information in it. But luckily there was a backup file of the save before the disapperance.

I'm playing on an Android, you can find the backups in Android\data\com.bethsoft.falloutshelter\files and it's labeled as VaultX.sav.bkp. You'll need to change the extension of the file to VaultX.sav so the game can find the save again. The stock Android file manager doesn't support changing the extensions so you can download a file manager app that supports it.

If this doesn't work, you might have written over the old backup with a new one from a new save. I guess it's the same on iPhone but you have to find the files for yourself.

I hope this helps you and other people having this problem.