4.4.6: Official Definition
4.X.X
[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.
X.X.6
[RFC3463] (Standards Track) from the The Internet Engineering Task Force (IETF) definition for codes that end with X.X.6:
A routing loop caused the message to be forwarded too many times, either because of incorrect routing tables or a user- forwarding loop. This is useful only as a persistent transient error.