Since the implementation of iOS 10, iTunes no longer seems to be able restore the data files associated with enterprise applications, as in mentioned in the Apple iPad in business document.
From the Backup section of this Apple iPad in Business document
"Applications you’ve developed in-house and distributed to your users with enterprise provisioning profiles won’t be backed up or transferred to the user’s computer. However, the device backup will include any data files the enterprise application creates."
In iOS 9 and below, we could backup our companies Enterprise apps in iTunes, and then we could safely restore the data contained in them, although we still had to manually reinstall the app itself.
This no longer seems to be the case, and we are experiencing the issue where we are wanting to replace some older devices, without a means of transferring data.