4.7.10: Official Definition
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.
This indicates that external strong privacy layer is needed in order to use the requested authentication mechanism. This is primarily intended for use with clear text authentication mechanisms. A client which receives this may activate a security layer such as TLS prior to authenticating, or attempt to use a stronger mechanism.