See if you can get at the line stats.
If the line stats are within tolerance then it's probably the router. IF they're borderline or up and down from good to bad then it's probably the line. BT can either resolve the fluctuation physically or force the lower profile to stop it trying to re-sync at a higher profile, then fail and have to re-sync at the lower profile repeatedly.
It's probably also worth checking your end for sources of noise and signal degredation. Such as:
Does the line run close to sources of magentic fields?
Are all extensions microfiltered?
Try any spare microfilters you have to route out a faulty/damaged one.
You could just ring BT but it's best to do the above yourself as it's all the BT engineer will do and if he finds a problem with your kit I.E your side of the master socket or anything connected to it, then it becomes a chargable repair not a warranty repair and you'll pay for it. For business it's £120 callout. Home is probably cheaper but still likely to be £80 or more for something you could do yourself for free.