From CL help page
What to Do if Email Program Will Not Connect
7 months ago Updated
We do have some reports of slowness in connecting to their mail client(iOS, Outlook, Android), sending mail, and receiving mail due to high traffic on the server. This is a known issue, and we expect a resolution within 72 hours. In the event you are experiencing these issues access to your email is always available real time www.centurylink.net .
We apologize for any inconvenience, appreciate your patience, and thank you for being a Centurylink Email Customer!
CL is aware of the situation, but appears they have done little to correct it. I have a legacy q.com as well as a centurylink.net account for my wife and myself. I’m only seeing it with the q.com accounts. This may be due to setting them up as IMAP when they were originally POP. I changed them back to POP and they are working for now.