All, I have this same problem and has just solved it on my iPhone.
I read up on the problem at att.com/esupport and arrived at the link below:
https://www.att.com/esupport/article.jsp?sid=KB413495#fbid=ahhj00ALH45
"If your email address is linked to your AT&T Access ID, changing your AT&T Access ID password automatically changes your email password to the same password.
If you use your email address as your AT&T Access ID, changing your email password automatically changes your AT&T Access ID password to the same password."
I have a ATT Uverse (for my internet access) acct and could not log on so I requested for password reset. They sent me temp password and I had to change my password to my Uverse acct. I use my att.net email as the log on for my Uverse acct. Per att instructions above, my Uverse acct is linked to my att.net email, so now my att.net email pw has been changed to the pw for my Uverse acct.
Accordingly, go into your iPhone Settings, Mail, Contacts, Calendars, choose your Att.net mail acct and change your password. In my case I changed it to the new pw I had set up for my Uverse acct and it works.
Before doing this, I had also added new servers as shown below. The way I see it because your iPhone will try in succession to log on to each server from top to bottom of the list, it's best to add all the mail servers.
smtp.mail.yahoo.com
smtp.mail.att.net
outbound.att.net
Please note that I did not have to add "imap.mail.att.net" and my Att.net mail on my iPhone still works.
Hope this helps.