Symptom
The Work Offline option under the File menu is grayed out in the Contributor Web Grid. 
 
Solution
The Offline Users is defined in the CAC under the Applications Rights:
Contributor Administration Console --> Datastores --> {Datastore_name} -->
Applications --> {Application_name} --> Development --> e.List and Rights --> Rights

Note:
- When selecting the Role for Offline Users (clicking on the ellipsis -- the button with the three dots), although the interface allows you to select multiple Groups, Roles, or Users, only one is accepted by the Admin Console. If more than one is selected, a message will come up to advise you of this.
- From the Online Help under Configuring the Contributor Application:
If the Prevent off-line working option is on, users cannot work offline. Offline working is possible only when cache on the client server may be used, but the client side cache does not have to be enabled.