What causes a bounce message that says, "Destination server rejected recipients"?

That error message is generated by our servers when they successfully connect to a mail server in order to deliver an email, but receive a permanent error when providing the recipient address to the destination mail server. In other words, the destination mail server that we are delivering to does not accept the message based on the "To" address of the message. This typically means one of two things:

1. Sometimes when a domain begins using our services, the mail server will see that the MX records point elsewhere (i.e. to us rather than directly to that mail server), and the mail server will assume that it should not accept email for the domain. This is particularly common when the MX records are updated via a web-based control panel that controls both the DNS records for that domain and the mail server itself. This problem can usually be solved by a small configuration change on the destination mail server, to tell it that it should continue to accept email for the domain, despite the MX records pointing elsewhere. These text files are different on different mail servers, but it is typically the /etc/localdomains or rcpthosts file. Also, some web-based DNS control interfaces have an option in their DNS settings to automatically make this change for you.
2. The email account itself may not be one which the server recognizes. Make sure that the users you have listed on your mail server are correct and complete.