When trying to enable Enterprise Features, the page comes up with a "Failed!" result. (No kidding - they added the exclamation point.) When you try to activate it again, you get this message:
An existing request to enable the Enterprise feature is in progress. To check the status of this request, go to the Timer Job Status page in Central Administration Operations and check the status of the Office Server Enterprise Features Upgrade Job.
When you check the status, it also says failed.
To fix this, I just restarted the Timer Service on each server in the farm. This kick-started the process and the upgrade job finished with success.