Three email rejection messages were reported to us several times recently:
"Your access to submit messages to this e-mail system has been rejected"
"You are not allowed to connect"
"Recipient address rejected"
These seem to have a correlation with Microsoft/Exchange recipients. We determined that the first two are likely issues of IP reputation, and so we've put in place rules to ensure that we retry delivery from several IPs before bouncing those back to the sender.
The third case (Recipient address rejected) had been tested under the same conditions for several hours and found to not be related to IP reputation at all, but to be an issue with Office 365/Exchange servers. It may be as simple as the recipient no longer existing at that domain, or as complex as an unknown misconfiguration by the recipient party (or their IT department). For the time being, we're considering that to be a legitimate bounce error that we cannot assist with. You can read more about that here: https://docs.microsoft.com/en-us/exchange/mail-flow-best-practices/non-delivery-reports-in-exchange-online/fix-error-code-550-5-4-1-in-exchange-online