I know it's not the answer you're looking for, but my daughters have mail.com accounts for their less important stuff. As long as they're signed into their accounts and have the browser window open on the taskbar, a single-note bell sounds each time an email arrives.
I use incredimail as I can have all my AOL & MSN e mail accounts on there & it just lets me know when I have new mail at any time, or a time period specified by myself.