Exchange Hub Transport Rule Ignored for local NDR reports

I'd tweak the costs myself:

"If you have multiple connectors, especially a connector that has a * in the address space (for sending email via your ISP) then you need to adjust the cost carefully. The wildcard SMTP connector with the * should have the highest cost, SMTP Connectors pointing to internal servers should have the lowest (so that they are used first). If you want to load balance the connectors then you can set multiple connectors at a cost of 1."

So I'd raise the cost of the postini connector to 2 so everything tries the Microsoft Domains connector first and then when it notices the specific address space goes to the postini connector.

The clue is in the NDR you received: The recipient's e-mail address was not found in the recipient's e-mail system..

If you are sending emails and getting this NDR, you have either typed in the wrong email address or the email address doesn't exist on the server you are sending to.

If people are getting this message when they email your users, check the email address or alias exists on your email server. Also check if you have any address list filtering set up with a third party provider (such as MessageLabs) where you have to provide a list of all valid email addresses, and if somebody sends an email to a person not on this list, the message is bounced.

Edit

The 5.7.1 message you are getting means you are not authorised to send email to the remote server (slight tangent - this Microsoft KB article on SMTP status codes is very useful, and definitely one to bookmark).

The reason you are getting a not authorised from the remote server could be several things. You could be on a blacklist, or the remote server might have other rules defined that are rejecting your message (intentionally or otherwise).

If it's just 1 domain you're having a problem with, at this point I'd be inclined to get in contact with them on the phone or on another email address if you're able to get through on that. Let them know you're having a problem sending them mail and ask for the message to be passed onto their IT department. There's a possibility you'll be ignored, but you might get lucky - it does happen.