Your phone line has call waiting, so whenever you get a call when you are online it messes up your connection—you get disconnected, or your downloads get corrupted or interrupted.
Disable call waiting in /etc/wvdial.conf. This option disables call waiting globally:
Dial Prefix = *70,
This disables it per phone number:
Phone = *70,1234567
You can add another comma or two to give it more time to take effect before dialing the number, if necessary.
The V.92 modem standard allows for more options than merely disabling call waiting: ignore, disconnect, or place the Internet connection on hold and take the call. The last option requires using an ISP that supports this. You'll need a modem that supports these features to make them work.
man 1 wvdial
man 5 wvdial.conf
man 8 pppd