You should use a [data volume container](https://medium.com/@ramangupta/why-docker-data-containers-are-good-589b3c6c749e#.uxyrp7xpu) for `/var/mail` to persist data. Otherwise, your data may be lost.
If this migration implies a DNS modification, be sure to wait for DNS propagation before opening an issue.
Few examples of symptoms can be found [here](https://github.com/tomav/docker-mailserver/issues/95) or [here](https://github.com/tomav/docker-mailserver/issues/97).
This could be related to a modification of your `MX` record, or the IP mapped to `mail.my-domain.tld`.
If everything is OK regarding DNS, please provide [formatted logs](https://guides.github.com/features/mastering-markdown/) and config files. This will allow us to help you.