2 of my att emails are not working

We have several att email accounts. 2 of ours are not working properly - we've had sporadic issues in the past related to the Yahoo thing but usually only temporary. Now it's been 2 weeks and the accounts are continuing to prompt for password re-entry OFTEN - say password is wrong - so go through resetting password either to same or new - usually errors out at end of resetting process - sometimes it will go through and some mail comes in and then a day or hours later same thing. It's maddening. Now my computer and phone say one of my accounts is online and working but no mail has come in for 2 days and that is highly unusual. At this point I am not sure what to do or why this is happening. I have another mail account that never falters and is working fine. Please advise!!