Instead of writing this all out again, here's what I sent them that explains the issue in more detail:
We are getting sporadic, very large amounts of packet loss to everywhere (eg 20% to orcon.net.nz over 10 minutes). Pings using the tool on the Genius web interface also show timeouts when expected (just to rule out WiFi issues for certain). This has been happening since the Wellington issues mentioned on the network status page the other day (though may be coincidental). This occurs seemingly without pattern, at any time of the day or night. It seems to clump together though - there may be a few hours where it's occurring, and then a few where there are no issues.
Needless to say, this means that at times the internet is completely unusable (and at others just slow, and sometimes it works fine).
The packet loss starts from the first visible hop after the Genius (llu.bng1.nct.orcon.net.nz).
We are connected to the Johnsonville exchange (presumably LLU'd).
I have power-cycled the Genius several times, which has had no effect.
If it helps, I have noticed that normally, the ADSL sync speed is around 7600Kbps, but while this issue has been occurring, when the modem has been restarted at various points, it has sync'd at anywhere between 2200 and this value (or has failed to connect altogether). The upstream sync has remained stable at around 750kbps.
I can provide screenshots or data dumps of PingPlotter traces (or manual tracerts) or ping logs.
Here's a PingPlotter screenshot from the other day:

I'm guessing there are three potential causes, in no particular order -
Faulty wiring between (or inside) the house and the exchange (though the lines are underground on this street). There is no correlation with weather, and no one's been messing about with the internal house wiring.
Something wrong in the exchange (note, LLU as above, and not cabinetised)
Something wrong with the Genius
Any thoughts?
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