A writer for a magazine last year had his Gmail account hacked into. Aside from sending out spam, the hackers ditched every message accumulated over the past 5+ years. Everything was gone. Googlre couldn't even properly restore what he did have. He then contacted a vP at Google [who happens to be a friend] and managed to get back all [?] of the lost mail. But for the average individual, good luck.
What is suggested is to install a mail client on a computer and connect to your cloud mail provider [Gmail, Hotmail, etc.]. Configure the software NOT to delete the mail from the server after downloading it to the computer.
Eh voila. An instant backup.
Open the client mail software every once in a while to "backup" your mail.