Just to clarify what's going on...
The majority of emails get stuck in a queue. Sometimes you can send an email and it will go straight away, but there are quite a few domains for which emails simply get stuck.
The user firstly gets a message saying that their email is delayed, but they don't need to resend it. After about 2 days, the messages time out with an NDR error code of 4.4.7.
Also, what can happen is the emails are stuck in the queue for a long time (a few hours), then all of a sudden the queue will empty.
Thank you very much for all your patience so far.