Checking SNR and ATTN will depend upon the type of USB modem you have, and what the installed software provides in the way of diagnostics. As I recall, Thompson Speedtouch modems can be used with some software called Dr.Speedtouch which ought to give you the required line statistics. Some USB modems may well not be capable of providing this useful info. I say useful info because line quality can play a significant part in how well you can maintain an ADSL connection to your local exchange. It's a bit like a radio station - if you're a long way away from the transmitter, you get a poor signal and maybe you can't always hear what the announcer is saying. So it is with ADSL. Nice short route to the local exchange generally gives you a good strong signal. Low SNR equals weak signal, and means the slightest bit of interference may block your connection. High SNR can often cope with quite a noisy electrical environment. Roughly speaking, anything much below 6dB DownStream SNR is cause for concern. ATTN or Loop Attenuation gives an indication of the distance from the exchange in terms of signal loss. The further you are from the exchange, the higher this figure will be. Over 60dB DownStream ATTN is getting borderline.
Routers usually have the in-built ability to monitor line statistics without additional software. Some routers have more sensitive front ends in their modems than others, so can cope better with poor line conditions. As an example, routers with a Texas T1 AR7 chipset are good with low SNR and high ATTN.
Trying to find the cause of your particular problem appears to be getting harder as it seems your line drop is becoming more sporadic. Is it possible to try another computer or a different USB modem? Or even borrow a router maybe? Given you can be there at precisely the right moment, have you tried the trick with the portable radio yet?
Certainly being able to view the line stats can be very helpful. Once you can do this, make a note of DS SNR and DS ATTN - ignore US SNR etc. (This is UpStream). Now try unplugging each telephone device (and its filter) from the sockets in the house. Re-checking the figures after each one is removed - this will tell you if one of your telephones/filters is/are faulty or causing signal loss. Don't forget the fax machine and any telephone connection for Sky etc. I don't know where you're located, but in the U.K. newer phone installations often have a Master socket with an NTE5 type faceplate. Removing the lower part of this socket not only reveals the "test" socket, but automatically disconnects all other wiring in the house from the telephone line, at a stroke! Putting your modem or router directly into this test socket assures you of no problems from telephone devices throughout the house.
Hope that helps...
ROGER - G0AOZ.