Ever tried Thunderbird?
Don't know if it can download your mails though. But it should be able to update your inbox every X minuts.
Just took a look @ Thunderbird, you can download the message to your PC + make it check every X minuts. Loads of more options/add-ons are in there as well.
Gmail has a feature called offline mail which will download your mail for you and update every time you log on. It also secures your emails because you need to log in on your computer to access them.