Out of Office Assistant was missing from the Tools menu for a user. Mailbox is on Exchange 2007.
To fix, I used an updated version of instructions from here, as follows:
On the Tools menu, click Trust Center.
Go to Add-ins, choose Manage: Exchange Client Extensions and click Go...
Click Install, choose outex.ecf, and then click Open.
Click OK on the Add-In Manager, close Outlook, re-open.