Outlook Express, by default, hangs up after sending and receiving e-mail. To fix this, go to the Tools menu, then Options. Select the Connection tab. There, you'll find a checkbox that says "Hang up after sending and receiving". Turn it off, and that should fix the problem.
If the problem persists, go to the Tools menu, then Accounts. Select the Mail tab. Make sure there is only one entry in there... or if there are more, make sure they're all set to use the same dialup connection.