You can manually back up your webmail inbox or restore messages easily:

To Back Up:

  1. Log in to yourdomain.com/webmail
  2. Select Roundcube client
  3. Select emails > Click the More menu > Download (.eml)

To Restore:

  1. Log in to Roundcube
  2. Click Settings > Import Messages
  3. Select the .eml files you want to restore

Tip: For large backups, use IMAP with a mail client and export from there.