Hi
Firstly, I'd be very surprised to see an engineer using the more-or-less obsolete HAWK tester, for anything other than the TDR function. This function can 'see' a high-resistance fault better than the hand-held testers (EXFO or JDSU), that we currently use today .... especially a 'near-end' HR condition.
Now then, the problem that is dropping PPP session.
Our mandate as Openreach engineers, is to perform various industry agreed tests including ......
A PQT (Pair Quality Test - IE: The pair of wires that feed your house from the Telephone Exchange).
A DSL Close-out test ( This is the broadband test that logs-on to the ISP's radius and passes data back and forth for a pre-determined amount of time - industry standard is 5 mins, but can be set for longer if required).
An Eclipse/Fast Test2 test (Depends on how the task has been built, or how the tests is performed, but basically only tests the low-frequency phone side. As mooted, the test can also incorporate a further high-frequency test that will ping the router at various frequencies across the bandwidth).
A QLT (Quiet Line Test - used to listen for audible noise on the landline).
You are right in your assumptions that PPP can be lost whilst the router remains in synch ...... I would say (generically) in order of probability the fault is likely ............ 1) Router 2) HR fault 3) IP addressing settings (Static or Dynamic) 4) REIN.
However, you mention the engineer could see errors during his testing
This really boils down to the severity of the errors and what kind of
error it is ?? CRC or FEC ??
A further trick we use to magnify a potential issue is to ring the landline, or make an outgoing call on the landline (usually 17070) to see if the errors increment dramatically ... pointing towards a probable metallic fault somewhere.
I don't suppose you could post some router stats up so that the proper clever people on here can peruse, and hopefully identify an issue ??