* which version of Windows and do you have the latest modem drivers for that version?
* what type of modem?
- external - serial / USB / ADSL / cable
* when is the connection dropped?
- during an "idle" period or when active
<<<I was told to go to the Connections tab in IE and select "always dial my default.">>>
If using dialup, try changing that to "Dial whenever a network connection is not present" or, alternatively, connect/disconnect manually and set it to "Never dial a connection".