If your modem goes offline frequently, it may be due to a temporary lost of carrier. To lengthen the time before the modem will go offline after the carrier is lost, change the modem properties.
Open up the Control Panel
Double click on the Modem icon
Click on Properties (not to be confused with Dialing Properties) / Connection / Advanced
In the Extra Settings, enter S10=10
This will enable the modem to stay connected without a carrier for up to 10 seconds.