Technicolor TG582n cannot cope with long lines

[#1]

My phone line is 7.295km long with 57.5dB attenuation, as measured by BT.  I've an Openreach faceplate filter and no internal phone wiring.    It's not a bad line, the DSL will remain connected for days or weeks at a time, but with the Technicolor TG582n if there is a disconnection then there's almost always a period lasting several hours where the router will lose sync every 2-3 minutes and reconnect.  During this time the internet is essentially unusable.  By "lose sync" I mean "internet light goes out, broadband light flashes".  I tried two different TG582n routers and they both did the same thing.
Last week I bought a new router, a Billion 7800N, and it's solved my problem.  With the 7800N, if there's a disconnection the router just reconnects.
This is what my connection looked like with the Technicolor routers:

19 Aug 2013 11:30:45  02 Sep 2013 15:53:35   14d 4h 22m 50s  1920/448 kbit/s
02 Sep 2013 16:05:25  02 Sep 2013 16:37:25           32m 0s  13 short sessions
02 Sep 2013 16:37:25  02 Sep 2013 19:59:33        3h 22m 8s  router powered off
02 Sep 2013 19:59:33  02 Sep 2013 20:17:43          18m 10s  5 short sessions
02 Sep 2013 20:18:16  04 Sep 2013 16:29:13   1d 20h 10m 57s  1536/448 kbit/s
04 Sep 2013 16:30:06  04 Sep 2013 16:34:13            4m 7s  3 short sessions
04 Sep 2013 16:34:47  05 Sep 2013 10:06:13      17h 31m 26s  1600/448 kbit/s
05 Sep 2013 10:07:24  05 Sep 2013 10:49:34          42m 10s  26 short sessions
05 Sep 2013 10:49:34  05 Sep 2013 12:23:26       1h 33m 52s  router powered off
05 Sep 2013 12:23:26  05 Sep 2013 15:56:24       3h 32m 58s  103 short sessions
05 Sep 2013 15:56:55  06 Sep 2013 09:37:26      17h 40m 31s  1408/448 kbit/s
06 Sep 2013 09:37:26  06 Sep 2013 10:02:29           25m 3s  router powered off
06 Sep 2013 10:02:29  06 Sep 2013 12:20:35        2h 18m 6s  61 short sessions
06 Sep 2013 12:20:59  06 Sep 2013 17:22:52        5h 1m 53s  1664/448 kbit/s
06 Sep 2013 17:23:26  06 Sep 2013 23:14:12       5h 50m 46s  147 short sessions
06 Sep 2013 23:14:47  08 Sep 2013 13:35:22   1d 14h 20m 35s  1568/448 kbit/s
08 Sep 2013 13:35:58  08 Sep 2013 13:40:22           4m 24s  2 short sessions
08 Sep 2013 13:40:38  08 Sep 2013 23:53:56      10h 13m 18s  1568/448 kbit/s
08 Sep 2013 23:58:26  09 Sep 2013 01:10:23       1h 11m 57s  22 short sessions
09 Sep 2013 01:11:11  09 Sep 2013 09:43:52       8h 32m 41s  1536/448 kbit/s
09 Sep 2013 09:44:26  09 Sep 2013 12:38:02       2h 53m 36s  73 short sessions
09 Sep 2013 12:38:02  09 Sep 2013 15:41:04         3h 3m 2s  router powered off
09 Sep 2013 15:41:04  10 Sep 2013 14:43:02       23h 1m 58s  1504/448 kbit/s
10 Sep 2013 14:44:02  10 Sep 2013 17:47:31        3h 3m 29s  84 short sessions
10 Sep 2013 17:48:06  11 Sep 2013 05:52:13        12h 4m 7s  2784/448 kbit/s
11 Sep 2013 05:53:02  11 Sep 2013 07:33:18       1h 40m 16s  38 short sessions
11 Sep 2013 07:33:33  22 Sep 2013 17:47:49  11d 10h 14m 16s  2400/448 kbit/s
22 Sep 2013 17:48:32  22 Sep 2013 18:52:53        1h 4m 21s  29 short sessions

This is what it looks like with the Billion:

22 Sep 2013 22:17:28  24 Sep 2013 00:15:06    1d 1h 57m 38s  1824/448 kbit/s
24 Sep 2013 00:15:45  24 Sep 2013 00:17:06           1m 21s  1 short sessions
24 Sep 2013 00:17:33  25 Sep 2013 14:22:16    1d 14h 4m 43s  1696/448 kbit/s
25 Sep 2013 14:22:47  26 Sep 2013 14:29:38     1d 0h 6m 51s  1856/448 kbit/s
26 Sep 2013 14:30:03  30 Sep 2013 10:07:51   3d 19h 37m 48s  1888/448 kbit/s

The 25 minute "router powered off" was when the BT guy was checking the line.  The other "router powered off" bits were me leaving it unplugged to see if anything changed (one of the phone support guys recommended unplugging it for 90 minutes to allow the exchange to reset itself.)
The phone support people I spoke to said it could not be a router issue because I'd tried two routers.  I agree that it's unlikely two router's hardware would be broken in the same way, but maybe there is a bug in the Technicolor's firmware.  I only figured this out because I know a guy who used to work for an ISP; it would be good if your support people could be made aware of this possible issue so that other people on long lines don't get left thinking there's nothing they can do.
Also: the BT engineer said that the periods of disconnection every 2-3 minutes I was experiencing is just what ADSL routers do on long lines, and that I should be grateful I had any sort of connection at all. What a cock!

[#2]

57.5db attenuation doesn't sound right for 7.3km. My line currently reports as 58.5db attenuation, and can manage about 3600k sync speed (with a netgear dg834g v3).
The 582n might have benefitted from the 10.2.2.B firmware, which amongst many other things, contains a newer adsl driver than what's in 8.4.4.J.

[#3]

Why doesn't 57.5dB sound right?  What's your line length?
FWIW I think my sync speed is lower than it could be due to all the disconnections.
Where do you get the updated Technicolor firmware?

[#4]

From http://www.kitz.co.uk/adsl/max_speed_calc.php the calculated line length for that attenuation is 4.1km and for a line length of 7.3km you would be lucky to get any ADSL at all
Updated firmware is here http://products.plus-payh.co.uk/firmware/

[#5]

Most of those online speed calculators assume .040" (18ga) wire which attenuates at 13.8dB per km.
(57.5 ÷ 13.8 = 4.1)
As I understand it, BT's standard phoneline is .050" (16ga) which attenuates less.
PS thanks for the link, I'll try it out.

[#6]

I don't know the exact length of my telephone line, my router reports the attenuation as 58.5 db, a short road route to the exchange should only be about 3km according to google maps, so I guess the telephone line takes a longer route and/or is of worse than average quality.

[#7]

Mine's a few hundred metres longer than the road route.
I can follow the line on poles for a while, but then it disappears into the ground.
I live in a village, so I'm assuming there's a trunk line that's higher quality than the standard wire.