Depending on the downtime you probably won’t miss any. Most other email servers will simply retry up to a limit (defaults are different for different systems) Usually 4 hours is a safe bet. If you need more time than that (and I would recommend it anyway), set yourself up a mail relay/gateway to handle incoming mail. Then when the server is disconnected it will continue to queue the incoming mails for delivery until the server is reconnected (make sure the defaults for deliver time as mentioned above are not too small though). Then change things back over to not using a relay after you are done. (To set up relay requires either a dns change or an ip address change, though since you are changing locations, I assume a dns change is in order anyway)
If you use an external service to filter your incoming mail, then they are already queueing it for you, just find out what their delivery timeout is so you don’t exceed it.