Details

In order to back-up the emails stored in your online Yahoo account, you need to download them on your computer to a local folder. In order to do that, you need to define your Yahoo mail account in Zimbra desktop application. As Yahoo does not offer this option for free (if you have an Yahoo Plus account you can use POP3), you need Zimbra that allows you to download all your yahoo emails locally. When the emails are on your computer in a local folder, you can back them up using the Zimbra plugin from Backup4all.

How to configure Yahoo in Zimbra desktop application

Zimbra Desktop is an email client which allows you to synchronize the Yahoo! account including: mails, contacts, and calendar items.
  1. Open Zimbra desktop
  2. Press Add new account.
  3. From the Account type list, select Yahoo!
  4. Type your account details as asked.
  5. Press Validate and Save.

How to configure Backup4all

Once you have your Yahoo emails on your local computer, you can configure Backup4all to automatically back them up. To do so:
  1. Download the Zimbra desktop plugin for Backup4all from this download link
  2. Install the plugin in Backup4all: go to Tools->Plugins->Add
  3. Go to File->New Backup
  4. Type a name for your backup in the Backup name field.
  5. Choose a location where you want to save the backup. Press Next.
  6. From the Selection of files and folders list, choose Zimbra desktop. Press Next.
  7. Choose how do you want to backup.
  8. Press Save and choose Save and run.


How to backup Yahoo! emails using Thunderbird

Another solution is to use YPOPS!, but it works only on computers running Windows XP. After YPOPS! is installed you will need to configure Thunderbird so that it will include your Yahoo Mail account as a POP3 email account. This way all your emails will be downloaded from Yahoo Mail to your local computer. If you want to keep a copy of your email messages on Yahoo Mail too, make sure the option "Leave a copy of messages on server" is enabled (detailed in the steps below). Steps needed to configure Thunderbird with YPOPS!:
  1. Open Thunderbird and click "Tools"->"Account Settings"
  2. Click on "Add Account"
  3. Choose "Email Account" and click "Next"
  4. Type name and email address in the associated fields and click "Next"
  5. Choose POP and type "localhost" as the incoming server (without the quotes)
  6. Depending on your preferences check or uncheck "Use Global Inbox"
  7. Click "Next" - if your username is not already there by default, add it
  8. Click "Next" - add details on how you want your "Account Name" to look in Thunderbird and click "Finish"
  9. Scroll down to the bottom of the "Account Settings" pane and click on "Outgoing server (SMTP)"
  10. Click on "Advanced" and after that on "Add"
  11. Type 127.0.0.1 as the outgoing mail server and leave the default port to 25
  12. Check "Use name and password". This is Thunderbird’s way of enabling authentication
  13. Type your Yahoo user name as username@yahoo.com
  14. Click "No" not to "Use secure connection" and then "OK" twice
  15. Click "OK" on the "Server Settings" tab
  16. Do not check "Use secure connection (SSL)" or "Use secure authentication" and click on "Advanced"
  17. Choose where you want your emails to go in the POP tab.
  18. Click on the SMTP tab and click on the drop down menu and select 127.0.0.1:25
  19. Continue modifying any of your preferences in the account and then click on OK.
Perform a Send and Receive to get all your emails from your Yahoo account. The first time you try to access the account, Thunderbird will ask for the password.
After that, you need to create a backup job using the Thunderbird plugin from here.
The backup will run and your Thunderbird emails and settings will be backed up to the designated destination.

Applies to:

Backup4all 4
Zimbra desktop 7.x
YPOPs! 0.9.5.8 or higher
Mozilla Thunderbird 2

Reff: http://www.backup4all.com/kb/how-to-backup-yahoo-emails-244.html