The error message itself is somewhat clear: communication between two mail transfer agents (MTA) has been failed. The key to this problem is not the exact error message, but which server generated it. You could detect this by the last (top)
Received: header of the attached headers of the bounced message & the first (bottom)
Received: header of the bounce itself.
If we have the simplest situation; MUA -> sender MTA -> your MTA -> mailbox; this kind of error may occur most likely on the sender MTA, when it tries to connect your MTA. Therefore, while suggested in the comments, this wouldn't even appear in the logs on your mail server. At the most there could be two events from connect & disconnect. Also, if mail from anywhere else is arriving normally, it's unlikely that this one sender domain would be treated differently.
When you can limit the problem to a single server:
- Someone should examine the logs on the originating server; the one that sent the bounce message. If the server is on the sender side, you don't even have access to these logs, and you couldn't do any testing either; pass the instructions.
- Test that the sender MTA gets correct MX records for the recipient domain.
- Test that connection to this
mx.example.com:25 can be established, for example that you get the correct SMTP greet message when trying to telnet your MTA
:25 from the sender MTA.
- Check routing between the servers, e.g. with
If the problem is somewhere else, all the same applies to that server and the next MTA.