You should use a [data volume container](https://medium.com/@ramangupta/why-docker-data-containers-are-good-589b3c6c749e#.uxyrp7xpu) for `/var/mail` for data persistence. Otherwise, your data may be lost.
### What about backups?
Assuming that you use `docker-compose` and a data volume container named `maildata`, you can backup your user mails like this:
docker run --rm \
--volumes-from maildata_1 \
-v "$(pwd)":/backups \
-ti tvial/docker-mailserver \
tar cvzf /backups/docker-mailserver-`date +%y%m%d-%H%M%S`.tgz /var/mail