we are having the same problem but context is a little different. We're running on a 2012 R2 Hyper-V virtual machine. We're using Outlook 365 and at approx 06:30 PM right after an SQL Server backup of all databases all user's cached Outlook data files (.OST) disappear. This means that the next morning there's going to be massive downloads of Outlook .OST files which will slow down the system for the entire morning.
During the night we run Veeam Agent for Windows 2.0 backups of our virtual machine (from within the VM). I checked registry settings for key HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Control\BackupRestore\FilesNotToSnapshot\OutlookOst and I also have the following value: "$UserProfile$\AppData\Local\Microsoft\Outlook\*.ost".
Extensive Google searches have not yielded anyone else except Veeam users as having this issue. This leads me to suspect that just maybe Veeam is somehow modifying VSS behaviour and consequently provoking the deletion of the cached Outlook .OST files.
Any comments are welcome.