BUMP! Still having this problem and it is causing the outbox to fill up. Please help!!

Generally, from my experience, it means that either the server on the other side is not a mail server. Have you tired doing a check of the mx records for the respective emails?

Same problem here. Happens only with multiple recipients. Does not seem to happen when only one recipient in the email. I don't think it's the MX records as we have tried different DNS resolvers, no change, and when testing we can always telnet on port 25 to the exchangers listed in the bounce message (SMTP logs), however, that is some time after the inital delivery attempt and one exchanger at a time, not multiple as would occur with multiple recipients and multiple delivery threads occurring.
I'm going to try reducing the delivery threads to 3 (from 10 we had it set to), then possibly just one thread (temporarily) and see if that helps.
I think this is an ASP or .Net issue.
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Warren

Fatal SMTP error when talking to smtp.ipapp.com.: 550 All recipients have been rejected by server

Delivery History Follows:
[DLVR 000590 30-04-12 09:13:31] Delivering item 30014
[DLVR 000590 30-04-12 09:13:31] Resolving MX records for domain esagelink.com
[DLVR 000590 30-04-12 09:13:31] Retrieved 1 MX records for domain esagelink.com
[DLVR 000590 30-04-12 09:13:31] Delivering mail to 1 recipient(s) at domain esagelink.com using exchanger smtp.ipapp.com.
[DLVR 000590 30-04-12 09:13:34] ERROR: The operation is not allowed on non-connected sockets.

Note the exchanger that the system is attempting to contact... not the correct one. like the rest, this only occurs during the send of multiple emails

Actually I can telnet into smtp.ipapp.com on port 25, and mxtoolbox says smtp.ipapp.com is the exchanger for domain esagelink.com.
You are getting "ERROR: The operation is not allowed on non-connected sockets" which is the main issue here, and only when sending to multiple recipients, but I don't think it's because the exchanger returned by the mx lookup was wrong.
I think this is a bug in ArgoSoft Mail, or in Microsoft ASP or .Net components, but I don't know and if that is the problem, we're at the mercy of ArgoSoft and Microsoft to fix it.