SQL Server Version : 9.00.5057

 User Database Maintenance Plan.Full Backup of User Databases which was running successful for quite long time, all of sudden started failing with error below:

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Date 7/28/2015 7:00:01 PM
Log Job History (User Database Maintenance Plan.Full Backup of User Databases)

Step ID 1
Server Wsrver
Job Name User Database Maintenance Plan.Full Backup of User Databases
Step Name Full Backup of User Databases
Duration 00:00:34
Sql Severity 0
Sql Message ID 0
Operator Emailed
Operator Net sent
Operator Paged
Retries Attempted 0

Message
Executed as user: Wsrver\SYSTEM. eter.  
End Error  Warning: 2015-07-28 19:00:34.91     
Code: 0x80019002     Source: OnPostExecute      
Description: SSIS Warning Code DTS_W_MAXIMUMERRORCOUNTREACHED.  
The Execution method succeeded, but the number of errors raised (2) reached the maximum allowed (1); resulting in failure. 
This occurs when the number of errors reaches the number specified in MaximumErrorCount. Change the MaximumErrorCount or fix the errors.  
End Warning  DTExec: The package execution returned DTSER_FAILURE (1).  Started:  7:00:01 PM  Finished: 7:00:34 PM  Elapsed:  33.297 seconds.  
The package execution failed.  The step failed.

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Did you tried changing the "MAXIMUMERROR COUNT" value ? also what is getting triggered for "OnPostEXECUTE"  ?

Raising the level for the number of errors accepted sounds like the wrong solution to me. Already 1 error sounds too much for me. You better dig around to find where they can have hidden the error messages.

Or, while you are at it, throw out the maintenance plans, and install better stuff from http://ola.hallengren.com

There are no changes made in respective to SQL Server. The maintenance plan was executing fine for last one year.

All of sudden it started failing. If I recreate a new maintenance plan which performs the same as existing maintenance plan, it works fine, without the MAXIMUMERROR COUNT value being changed.

Seems like the SSIS package feel that SQL Server returned a lot of error messages. Anything in the SQL Server errorlog fie?