Hi Hesthekeeper,
If you line is disconnecting at about the same time each night it does sound like you either some REIN (Repetitive Electrical Impulse Noise) or some SHINE (Single Isolated Impulse Noise) affeting the line.
Have you had the helpdesk organise you a specialist engineer to come out to investigate the problem, as it might not be something local to your property that is affecting the line, it could be anything between the exchange and the phone socket.
Markp