I have a big e-mail box over at my provider. I receive a lot of e-mail every day (over 100), which are distributed into different imap-folders by thunderbird. The problem is that thunderbird must be running (offcourse) to be able to it's job. And for thunderbird to run, my (home)computer must be running.
I used to use maildrop on the IMAP server I administered. It worked well and syntax was easy to follow, but since it involves changing the local mail delivery agent at your provider might not be an option.
http://www.courier-mta.org/maildrop/
Patrick