4.7.13: Official Definition
[RFC3463] (Standards Track) from the The Internet Engineering Task Force (IETF) definition for codes that start with 4.X.X:
A persistent transient failure is one in which the message as sent is valid, but persistence of some temporary condition has caused abandonment or delay of attempts to send the message. If this code accompanies a delivery failure report, sending in the future may be successful.
[RFC3463] (Standards Track) from the The Internet Engineering Task Force (IETF) definition for codes that end with X.7.13:
Sometimes a system administrator will have to disable a user's account (e.g., due to lack of payment, abuse, evidence of a break-in attempt, etc). this error code occurs after a successful authentication to a disabled account. This informs the client that the failure is permanent until the user contacts their system administrator to get the account re-enabled. It differs from a generic authentication failure where the client's best option is to present the passphrase entry dialog in case the user simply mistyped their passphrase.