I can't tell which email system or app but here, I use Thunderbird across machines without any trouble. However even with no troubles, it still means I backup what I can't lose. In Thunderbird it's widely documented how to backup and restore emails.
I had my email, including my Pop email, wiped out the end of January without prior notification/explanation. Tried rebuild to no avail. Some messages appeared in documents but not many. Now email is deleting emails and only leaving headers. Is anyone else having these difficulties?

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic