Just a few thoughts:.
If you haven't done so already, try shutting down MLO fully (double-tap the home button then swipe up on the open apps, including MLO) and then restarting it. You could also try a soft reset (ie not wiping data) on your phone, in case it's some kind of bug with the face-recognition.
Do you have them sync'd with MLO on Windows? I do all my backups that way. You could then delete and resync your profiles. MLO's own Cloudsync would be another way to restore an uncorrupted copy, if you have an MLO Cloudsync account.
I've just discovered that you can create manual backups of your profiles from your iPhone, but that won't help if you haven't been backing them up and they're already corrupted - I'm mentioning that to draw it to the attention of other iPhone-only users, so that they can keep backups in case the same problem happens to them.
Stéphane