A common cause of disconnects is line noise. As a test, try unplugging EVERYTHING connected to your phone lines: caller ID boxes, extension telephones, cordless telephones, other modems, fax machines. Also unplug your laser printer from the AC wall outlet. We have learned that many telephone line 'surge protectors' or 'noise filters' will seriously impair your phone line. Also avoid any type of "splitter" on your line. Test your connection with the modem being the ONLY thing connected to your phone lines. If the problem goes away... then you have something in your house causing you to disconnect. Do not route the phone line within three inches of any electrical cord or extension cord, or PC CPU cable, Printer cable, Monitor cable, any electrical appliance or power supply. Especially avoid laser printers, cordless telephones and uninterruptable power supplies (UPS's). Inductance from electrical lines and radio transmitters can wreak havoc with phone lines. 

If the line noise is not being induced inside your house it may be induced in the cable somewhere between your house and your local telephone exchange central office. Your line may have a one or more of conditions the telco calls 'bridge', 'ground loop', 'cross talk', or 'bad loading coil'. Any of these conditions will cause random noise and unpredictable disconnects. 

For noisy lines, try increasing a setting that tells the modem how long to wait (in tenths of a second) before hanging up when it loses carrier detect. This guard time allows the modem to distinguish between a line hit, or other disturbance that momentarily breaks the connection, from a true disconnect by the remote modem. See below:
 

If the above seems to help, contact your phone company and request the line be checked for noise at the network demarcation block at your house. Do not let them just check the line from the central office end, ask to meet the repairman at your house and get him to report the results of his tests to you. If you encounter resistance from them because you have a modem, call back and tell them your fax machine is not working well with your phone line. 

Sometimes defective cables and loose connections will cause disconnects. For external modems, if the serial cable is old, adapter pins bent, or cable cracked, replace it or try another one. Make sure your serial connections are TIGHT. Examine your telephone cable between the wall jack and the modem, or better still try replacing it. If portions of the telephone cable between the network interface and your wall jack have been stapled to the wall, examine the cable carefully. If possible try another jack, or the jack on the telco network interface itself. 

If you have call waiting, remember to add a *70 (or other code, depending on your phone company), to the front of the phone number to disable call waiting. Otherwise every time someone calls you, the modem may disconnect. This can also be specified under Dialing Properties in the Modem Control Panel.

We have a 30 minute idle timer, which means if you leave your computer logged in, but do nothing which exchanges data over the link, then your call will be disconnected after 30 minutes of idle time. An example might be when you are reading or answering your email. Even though you may be typing a reply, all activity is taking place on your computer, so this will not cause any data to be transmitted. After 30 minutes  the call will be disconnected. Windows 95 / 98 has a 20 minute time-out setting, but this should warn you before it actually disconnects. You can adjust the setting in the Internet Options Control Panel. Look under the Connection Tab and Settings.

Although rare, your modem may be set up to automatically disconnect after a certain period of inactivity. Go to the Modems Control Panel, click Properties for your modem, then the Connection tab. Uncheck the idle time-out box.

Generally, you should hold a connection for as long as you wish.... there will ALWAYS be an occasional disconnect, we are after all, dealing with phone lines pushed to the very limits of their capacity when using the latest generation of modems. But you should not get repeated disconnects, if you do something is wrong and you should methodically follow the steps above