Subaccounts No Longer Logging in from Apple Mail

[JillH]

I have one main account and three subaccounts that I access via Apple Mail (using Mac OS X 10.6.8).  These accounts have worked fine for years.  Starting a few days ago, the subaccounts could no longer log into Verizon to retrieve mail.  Apple Mail asks for the password for each one when it tries to take the mailbox online and I enter it correctly, but it doesn't work.  Apple Mail continues to reopen the password dialog box until I get fed up and click "cancel."  I just logged into the subaccounts directly in Verizon webmail, and they are active and receiving mail.  Logging in also confirmed I am typing in the correct passwords. 

My main account is working fine.  It receives and sends email.  How can the main account keep working while three subs all go offline permanently at the same moment. 

Before anyone asks, I have shut down and rebooted multiple times.

Help, please.

[electrosaw8od]

I have encountered the same problem with my PC. I am running Windows 8.1 and internet explorer 11.