Your line is obviously unstable. Changes in attenuation should not occur.. and your sync speeds seem to vary.
Even when you say that the connection is fine at times, your stats would say otherwise.
Routerstats allows you to continually record your linestats and show when errors occur, the graphs can sometimes give us further clues as to what is going on. It does not interfere with your actual connection. It is a very useful diagnostic in identifying problems with low SNR and REIN.
The periods where you cant get connection (slow flashing light on the router), indicate that your SNRM is too low to be able to sustain or attain synchronisation with the exchange. I suggested last week that this should be reported to your ISP.
Although we've suggested several times that you connect direct to the test socket behind the NTE5 can you please confirm that you have done this and provide a fresh set of stats from there.
Problems such as this can be a result of faulty wiring either internal or eternal - you need to ensure its not internal.
Intermittent faults behave like yours.. they can be fine for a while then suddenly get worse, then recover again. They will not go away totally until the cause is found.
Your attenuation is increasing which isnt a good sign - as mentioned in previous posts this should remain fairly static, and points to degradation of the line somewhere.
Weve given you links for the tools we use, and tests to eliminate that the problem isnt internal, theres also lots of information on the main site which explains whats going on and how the line should behave. We are more than happy to help you interpret the results which can often identify where the fault lies... because we understand this part only comes through experience and knowing how to read the results. From what we see just so far we can see there is something wrong with the line.. but we are trying to help you identify were the problem is.