I've seen the Steam version delete save files if you put them into the save folder and then open the game's launcher (some sort of verification system). Are you using cloud saves? I heard those were unreliable as well.
If it's happening a lot, then your best bet might be to go into your save folder to make a back-up of the save files inside; they're usually here:
C:\Users\[user name]\Documents\Square Enix\FINAL FANTASY VII Steam\user_######
When you need to restore back-ups, open the game's launcher first and then place the save files back in there. They should persist if the game is saved in one of them during that same session, but it sounds like you're losing them anyway. You might need to keep taking backups of the save folder after every session unless the source of the problem can be tracked down. This'll at least let you play the game in the meantime without losing progress.
