apple mail

Computer 1: Mid 2012 MacBook retina; High Sierra 10.13.6; Mail 11.5

Computer 2: Mid2009 MacBook Pro; Yosemite 10.10.5; Mail 8.2

Both computers are having problems sending email through CenturyLink. They receive mail just fine, but on sending mail, we get a message that the password can't be confirmed. We can send from iPad, iPhone, or using CL web page; only the MacBooks are affected. The retina also has iCloud and Gmail: those accounts can send and receive with no issues.

We have deleted and re-entered passwords under 'Internet Accounts' in the System Preferences and/or in the Mail app. Sometimes that works for a while.

I called CenturyLink and they said that it is a Mac problem (of course) and offered to change the password on their end. After that, the Retina has been able to send (for ~72 hours) but the Pro has gone back to the same apparent problem.

I suspect that this is a CenturyLink problem, but I need the vocabulary to battle my way through their phone tree. They are content with getting email to work at the moment but I want a solution that will continue to work tomorrow.

All suggestions appreciated.