4.4.4: 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.X.X:
The mail system was unable to determine the next hop for the message because the necessary routing information was unavailable from the directory server. This is useful for both permanent and persistent transient errors. A DNS lookup returning only an SOA (Start of Administration) record for a domain name is one example of the unable to route error.