Has this just started or has it been doing it for some time?
Have you changed your password recently?
Have you changed any settings recently?
Have to deleted and re-set up the account?
Are you able to send and receive via webmail using this link?
Do not make any changes at this stage.
It is not unknown for the BT servers to have problems that get cleared in a day or two so I would suggest that you just leave things as they are to see if it sorts itself out.
If the problem is still there after a couple of days post back.
If you have not changed your password this should not really affect you but it might be worth checking since you have deleted and reinstalled the account twice.
When you change your BT password on an iPhone it might only change for INCOMING mail.
To change the outgoing mail password you have to go into Settings; then scroll down to Mail, Contacts, Calendars.
From there select the BTinternet account and select the account where it is listed under IMAP.
You will find the details for the account and can change the password for the Incoming Mail Server there, but the outgoing mail server only shows SMTP and mail.btinternet.com
If you tap on the outgoing mail server it shows that it is 'on'. You have to tap on that Primary Server in order to find where the Outgoing password is hidden so you can update it.
You should also check the settings as per this link.
If they are different to the above, do not change them at this stage. Report back what they are and leave them.