If your DNS is set correctly and you have your email accounts setup properly, most likely the sender is aware of why the delivery failed. Usually, if our servers rejected an incoming email, the sending server would bounce an email back to the sender with an error message stating why the delivery was rejected. If you can get that message with the error, and provide it to us, we will be happy to diagnose the issue.
However, if there is no bounce message, there are 3 possible scenarios:
1. Their mail server is still trying to send it, and will most likely bounce the error after it has exhausted the amount of attempts it is configured to make.
2. Their mail server is delivering the email to some other server that is not part of our service, and they should investigate the logs to find out why. The other possible reason is, if you recently updated MX records, they may still be propagating over the internet.
3. Their mail server is somehow broken or is not sending emails at all. They should investigate it to find out the possible cause.