Were you syncing these contacts with a Microsoft Exchange server? If so, there have beenreports of contacts missing emails and/or phone numbers when they have been synced with Exchange and is due to a security feature of Exchange where the information is meant to be confidential and secure. We’re still investigating to see if there is a way to still access the full contact information or whether iOS or the Exchange configuration locks it from being copied. iExplorer gets the contacts data from an iTunes backup, so that missing information is most likely not even included when iTunes backs up the device. If you are currently extracting the contacts from an unencrypted backup (no password protection), please try making an encrypted backup and see if it will display and transfer all of the contacts information. To make an encrypted backup, you just need to check the box to Encrypt your backup on the Summary page for the device in iTunes (the first screen that appears when you select the device in iTunes) and choose a password. The AppleCare article below explains how:
Then, that will automatically make a new iTunes backup once checked and a password confirmed, and once the backup is completed, just close and reopen iExplorer and go to the Contacts section to see whether the missing information is there now and transfers okay.
Unfortunately, if making an encrypted backup doesn’t help, I do not have any workaround for this. iExplorer will at least transfer most contact information, and then you would need to manually copy over any missing emails or phone numbers.