I've had this problem a number of times with a secondary ntl world e-mail address and I've found that editing the mailbox settings helped. Do this via
ntlworld.com - help - email options - add extra email boxes to your account(?) - log in with your main account - then click modify against the secondary account - edit the password then continue to save the settings.
This seemed to kick start it again. There may be a better way to do this and it may not solve your problem but I hope it helps.
I'm not sure if this is just coincidence but it stopped the annoying password box appearing every few minutes and started downloading e-mails again
HTH