I have experienced this problem over the years and have it again. All the fiddling in the world makes no difference. The only option seemingly is to sit it out and hope service is resumed. This can take varying amounts of time from hours to days. When waiting you have no idea whether service will or will not be resumed. This is totally unacceptable and BT seems to have a tin ear when the issue is raised. I don't know if anyone from BT monitors this site but after nearly 15 years with a BT email address I am close to switching despite the disruption this will bring. BT please sort it out!
Unfortunately this issue will never be sorted out.
BT is aware of the problem but either couldn't care less (it only affects a small proportion of its customers) or cannot do anything about it due to its technical incompetence.
I actually believe the latter is true. BT is such a bloated bureaucracy that it finds it impossible to correct technical matters like this. Perhaps BT has tried similar "fixes" in the past and discovered that this only gets them into more trouble.
It is significant that none of BT's telephone support staff are trained to give the true reason why this happens (the fact that a certain percentage of customers with BTinternet addresses have been allocated Yahoo servers and these are the one which go down regularly because BT cannot synch them properly).
No BT telephone support agent has given this explanation, though they have all given a dozen other explanations. All of them, of course, promise that they will definitely fix the problem, and of course none of them ever do.
I left BT in total frustration over a year ago. I could never go back to BT.
I still retain my BTInternet email address as it is on all my stationery, websites and documents scattered all over the Internet. So I can't afford to give it up. Unfortunately BT know this, which is why they are going to be charging me £7.50 a month for this ONE email address.
BT are a bunch of incompetent chancers.
So I will also relate, for example, how BT describes its £7.50 a month email address racket as a Premium Service, complete with a Premium Service Helpline (which never works because nobody has ever answere the phoned whenever I have dialled it. So ... guess what? I no longer dial it).
That is BT's definition of a Premium Service.
A racket, though and through, and impossible to fix itself!