It is NOT a password problem. If it was it would not have worked before or since so do not change your password. Doing so when the email system is not working as it should can cause more problems.
It is more than likely a BT server problem and when this usually happens it resolves its self in a few days. The best advice is to leave things as they are.
You could try turning your phone off and on again or leave it off over night and it might reconnect to a different server.
I find that when I check my inbox on my iPhone or my iPad, there is usually recent mail there. Then, for no reason, a box pops up saying 'Cannot get mail' and advising me to check the email settings. A minute later (or sometimes longer), it sends for mail and mail arrives.
I have no idea why this happens. I have learned to ignore it and do nothing because experience has shown that it will right itself. I can live with this, whereas changing my password and settings can cause endless complications.
I have had the same problem this week
Logging into mybt tonight it said there is increased security and my BTID had to change to my email address. Did this and claimed my BTYahoo email account so they now have the same password and I cannot use Mac/iPhone/iPad any more just WebMail.