The question is being raised for Exchange 2007. the below error message was received by one of the users. Let us know how to resolve it. I have checked the mailbox quota and found no issues. In message tracking mail flow and it shows as failed.
"There's a problem with the recipient's mailbox. Microsoft Exchange will not try to redeliver this message for you. Please try resending this message, or provide the following diagnostic text to your system administrator."