The exchange server for the database object "Public Folders" wasn't found in Active Direcoty Domain Services. The object may be corrupted.
I opened the configuration partition with ADSIEdit. Under Services --> Microsoft Exchange --> Exchange Org Name --> Administrative Groups --> Exchange Administrative Group --> Databases I had two public folder databases, 0261515011 and 0931127523. My Exchange 2010 server had a database associated with 0261515011. There was no database associated with 0931127523.
To resolve the issue I deleted 0931127523 with ADSIEdit.