Make a voice call and see if the sound is clear. Listen for pops, clicks or fading. These noises indicate interference which can cause data connections to be dropped suddenly and erratically. Make sure the plastic connectors on either side of the telephone cord are in good condition. The plastic clip must be intact, and the connector securely inserted into the jack or port.
Phone jacks can also be a problem.
Sometimes, phone jacks don't make a very tight connection, and jiggling can unseat them just enough to prevent connectivity. Check the connections by unplugging and re-plugging to make sure the connectors are seated securely. If a handset is connected through the modem, check for a dial tone. Connect a handset to the line, and see if there is a stutter three times when first picked up. If so, this could indicated there are voice mail services, provided by the telephone company, on this line.