Mail Transfer Agents (MTA) on the Internet will continue trying to deliver mail to your domain if your server is down, or if the domain is over its resources and unreachable. Some MTAs will notify the sender if not able to deliver an email within an hour however they will continue to retry the delivery. How long an MTA tries is configurable but most will try anywhere from 3 to 7 days. If after that time, the email is still undeliverable the MTA will give up and notify the sender of the failure.
