You can backup your Gmail account in several ways. To backup your messages in gamil using thunderbird, follow the steps given below:
  • Login to Gmail
  • Click on settings in the top right corner
  • Go to the Forwarding and Pop link or tab
  • Click on Enable Pop for all mail
  • Then again click Forwarding and Pop link or tab
  • Click on Keep Gmail's copy in the inbox from the drop down menu.
  • Click the "Save Chages" button.
  • Then open or download Thunderbird if you don't have
  • Once inside the Thunderbird mail window go to Tools =>Account Settings
  • Click the button 'Add Account'
  • Click Email Account and next
  • Fill in your name and your full Gmail address
  • then click Next
  • Choose POP and type in pop.gmail.com for your incoming server and click Next
  • Type your full Gmail email address as your incoming and outgoing email address, and then click Next
  • Click Finish
  • Click in the left pane the section that says “Server Settings”
  • On the right side of the new pane choose SSL and type in 995 for your port, the other options are semi optional.
  • Click Get mail, from Thunderbird.

It will take several days to get a complete backup, when it is finally caught up it will be really fast for future emails. You don’t have to leave the computer on just have Thunderbird open for a bit every time you have the computer on to allow the backup, and then close it when you get off.