There is a setting in Outlook Express, that allows one have his/her computer dial-up
unassisted, check for email, and disconnect automatically.
Now, sometimes people change it without realizing what it does.
To fix it, go to "Tools" (in Outlook Express), and scroll down to "Options" and click it. Click the "Connection" tab.
UNCHECK "Hang-up after sending and receiving." and click "OK". This should keep you online.