Your downstream noise margin should be more like 30dB not 3.7dB. Most
routers will be unreliable once you get below about 9dB. Try the usual
disconnecting everything (phones etc), just have the router only plugged
into the BT master socket, also try it without any microfilter in case
that's faulty. Try switching all mains appliances and non tungsten lights
in the house off, try moving leads around while you look at the noise
figures, you may have a dodgy lead.
I've just had an ISP arranged BT engineer visit to fix an intermittent
noise/disconnection problem that had got worse over a 2 month period, and my
problem was actually two it seems. One was an ancient street cable he
swapped over to a new one, that got me 6dB less attenuation. The other was
noise generated in my house by mains adapters running the router, switch and
a cordless phone and the fix for these was to wind 4 turns of the DC output
leads round ferrite rings (I did this after the visit). The 2 fixes
together gave me about 8dB improvement in noise margin. The orange ring
wire can be disconnected in the BT master socket (see
http://yarwell.blogspot.com/2005/08/adsl-tweaking.html) to improve some home
systems but mine was already disconnected it seems by the BT engineer that
fitted my ADSL in the first place 2 years ago when it was swapped over from
ISDN so I had nothing to gain there. I now get 44dB attenuation and 24dB
noise ratio on a 2MB connection, 512K used to be about 35dB noise ratio and
the figures are close on two routers I have (D-Link DSL-500 and Safecom
SAMR-4110).