I am adding my experience to the long list, just so that BT knows the problem is widespread and continuing. Yesterday and today, so far, I suddenly lost my BT Yahoo mail on my Mac with the now common password rejected message. I have no time to fix it so will use webmail meantime, but it just hammers another nail in the BT coffin.
Until April 2012 there were enough threads on password rejection to knit a large sweater but then the moderator closed the forum saying all was well. It isn't. I have been unable to access my bt mail since March except by logging on to webmail after which macmail behaves correctly for about 1 hour. Wasted £30 on a premium BT help service on this matter. Very nice guy but perplexed! This issue is not dead. I had the same issue with my iphone which was resolved in an Apple store. Is there now a fix for this utterly irritating situation? It does BT no credit whatsoever. Any chance of reclaiming my lost hours and £30? I think I know the answer to that one.
This started for me two days ago on my iMac. Changed password, looked for solutions on the net and tried them. Downloaded Thunderbird but that made no difference. Went into Parallels / Windows 8 (**bleep**) and downloaded Thunderbird but exactly the same result. Tried on my MacBook Pro and mail downloaded but it has been intermittently asking for password and rejecting it. (Thunderbird the same) Can't send mail either.
Rang BT this evening and after 13 minutes of messing about he tells me they are aware of the problem and to use Webmail!!
I have just joined this forum - I never knew it existed. It is helpful to find that I am not alone in experiencing this rpeated but intermittent password rejection by the BT server when using MacMail. The same password works fine when accessing webmail. Maybe BT just force us to look at their website to pick up the ads? If I could change to someone else, I would. BT always blame Apple; Apple blame BT!
I don't know if you are aware but BT are moving away from Yahoo for their email service sometime this year so hopefully this problem will stop.