If the problem persists, then you probably have a noisy line. Modems are sensitive and can detect noise you cannot hear. Call the local phone company's repair service and ask them to test your line to make sure it's clear. You're not asking them for a particular connection speed, you're asking for a clear line, for which they can test. They will give you the run-around at times if allowed to so do.
All noise comes from the analog end of the connection.
It is 2 digital phone lines each with it's own phone number. It can do 128k data using both channels, or 64k data through one channel while you talk on the other channel. It intelligently and seamlessly switches between the two. You can be online at 128k, pick up the phone to make a call and the modem will automatically go to 1 channel for data and switch back when you are done talking. Likewise, the phone will ring while you are using both channels for data, and when you answer the phone it will automatically switch the data to one channel, and back when you get through talking.