This is their reply:
The error that you are seeing is ESP throttling, and this occurs whenever the recipient’s email provider has received a large number of emails from a specific IP/sender in a short period of time. Due to this, they will not accept messages for a certain period of time (usually an hour; sometimes a day) until they have processed all the emails from the original batch sent. ESP throttling is a common occurrence in the email world, and we’re one of the few providers that actually show these notifications in the email logs.
The error code of “4xx” indicates that this is a soft, temporary bounce. Whenever we attempt to deliver a message and the recipient server returns a soft bounce, we will retry delivery for up to 8 hours in the following intervals: 10 minutes, 10 minutes, 15 minutes, 30 minutes, 1 hour, 2 hours, and 4 hours. These intervals are not able to be adjusted at this time.
This issue should clear up after some time. However, if you’re still not seeing any improvements, please reach back out! We’ll be happy to take another look at that time.
Well, this doesn’t gel with the fact that all Microsoft email services are blocking our emails (not just a few isolated ones). Will let you know how this unfolds from here, as it doesn’t look like I can do anything else right now.