I added 3 Exchange servers to our environment for Disaster Recovery purposes and once I did that an mail-enabled Public Folder quit receiving external email.  What happened is that the new servers were not running Exchange services because they were in stand-by mode only to be used in case of a failover event.  But the problem was that in Active Directory they were listed as active exchange servers and apparently whichever server is listed first in the below PATH is the server that will handle email for mail-enabled Public Folders.

To fix the problem you need to go to the following ADsPath using ADSIEdit and remove the server(s) that are not active. Configuration\Configuration\Services\Microsoft Exchange\CompanyName\Administrative Groups\First Administrative Group\Servers\ServerName\Information Store\Storage Group Name The ServerName is the name of the server you want to remove from the list.  The Storage Group name is the one containing the Public Store. Right click on the Public Information store on the right.  Find the attribute named "msExchOwningPFTree" and click the CLEAR button.