Problem: Internet Explorer does not prompt to disconnect the dial-up connection

You need to click start | settings | control panel.
Open the internet icon.
On the dialog box that opens, click on the connection tab.
Then click on the settings button.

If you have Internet Explorer 4.x installed
Be sure that the disconnect if idle check box is checked and set the time as desired.
Click OK to save any changes.
For whatever reason the disconnect prompt is tied to this function.
I suppose the logic is that if you don't care if your connection is idle then you won't care if there is an active connection when you end Internet Explorer.

If you have Internet Explorer 5.x installed
Then click on the advanced button.
Check the disconnect when connection may no longer be needed check box is checked.
Click OK to save any changes.