Intermittent fault since November

[#1]

Since moving from BT to Plusnet we have had continual faults on our telephone line, with loss of service for half a day to several days at a time.
By the time Plusnet  contact BT and they pass it to an engineer, the fault has corrected itself. They tell me there may be an intermittent fault at the exchange. The BT engineer says the only way he can trace the fault is to carry out a test while the fault exists. Because of the delay this has not been possible.
Can anyone suggest a solution, or do I have to return to BT?

[#2]

It can be very hard for an engineer to try to trace a fault that's intermittent. Ideally, I'd suggest letting us run a line test the moment the problem happens (post here and one of us should be able to arrange this). This will hopefully then give us an indication as to the location of the fault.