Q: Can I retrieve deleted messages on facetime

FaceTime messages are not specifically mentioned in the items that are stored in iTunes backups. The same type of data is also stored in an iCloud backup, so based on what Apple says is backed up, I would say that there is no way to retrieve them. But again, I am basing this own what I read in here.

http://support.apple.com/kb/ht4946

The only way to retrieve them without the use of a third party app, (if there are any third party apps that will do this) would be to restore from a backup, and that is if in fact they are stored in the backup.