The normal target SNR margin is 6dB. It is raised in 3dB steps if the line is unstable (too much noise). If the noise stops it is meant to drop again in 3dB steps back to 6dB. Each drop is said to require 2 weeks of stability. Sometimes the drops fail to happen.
You could ask your ISP to reset your target SNR margin to 6dB. Getting them to understand the request may take perseverance though and their may be a special form of words they need, e.g. can my line be retrained. Make sure the request is for the phone number associated with the BT as ISP line.
It is probably worth getting the error stats (CRCs, HECs, FECs) from the line first. The command to do that are modem specific, or try http://kitz.co.uk/adsl/frogstats.php
Is the bell wire disconnected? See http://www.dslzoneuk.net/socket.php?type=html