Due to concerns, confusion, tens of thousands of accidentally lost emails, and voiced concern from Compliance, the Backspace key to archive feature has been disabled by default and is now opt-in only.
To enable the feature again add the user to this group: Outlook - Disable Backspace Archiving (Exemptions)
The GPO should update within a couple of hours, and after a reboot, Outlook should allow the feature to work again.
To force it, connect to the user's computer and run: gpupdate /force
Note: This is a user-side GPO linked to the HFUsers OU.