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The incremental User Profile Service timer job was failing.

After looking around, I also noticed the User Profile Service would not start correctly.

The Forefront Identity Manager Service and Forefront Identity Manager Synchronization Service were both disabled for some reason.  I set them to Automatic.  They already had the SPFarm credentials assigned to them.

Now the User Profile Service starts correctly and the incremental job runs successfully.

References

Provisioning the User Profile Service Application

Forefront Identity Manager errors when starting the SharePoint 2010 User Profile Synchronization Service Application

Plan Security Hardening

Provisioning User Profile Synchronization