that line-noise can lead to dropped broadband connections, and 3COm are right to suggest it as a possible cause.
BT will normally test for a voice quality on the analogue line, and this isn't quite the same thing. Do you have anything else connected to the line - such as a fax or telephone answering machine? Such devices can routinely 'poll' the line, and this noise can result in a dropped connection to the broadband gateway. Try the router on the line without anything else, even a phone extension, being connected and see if things improve.