Some users have seen major improvements by doing this. Only the modem and regular phones should be on the line. The line should be completely quiet. If it is not then you have a line noise problem. Note, you may not hear noise every time.
Line noise tends to be intermittent.
All it takes is one burst of noise to disconnect. You may have to listen a number of times to hear the noise. Check the plastic lock tab on the phone cords where they plug into the wall and the computer. While the lock tab is not required to make the connection, if it is broken off you are very likely to experience connection problems since the natural force on the connector pins tends to push the connector out of the jack. We are in an area where there tends to be salt in the air from the ocean.