After a couple of weeks and with the schedule actions re-started without any Application Errors I am pretty confident that the root problem had to do with the Application Pool setting on the IIS 7 server.  

Just after changing the Scheduler entry for the Search Indexer from every 30 minutes to every two hours the system threw four General Exception errors with the root error being a timeout for method: System.Threading.ReaderWriterLock.AcquireWriterLockInternal.

This past Thursday after a user attempted to login the result was a "yellow screen of death" with the message: 

Server Error in '/' Application.
Exception of type 'System.OutOfMemoryException' was thrown.

The re-install of the DNN files and database has resulted in a much more stable website.