This problem has been driving me nuts as well until I discovered a setting in mail preferences under the composing tab. There's a choice for 'Sending New Mail from: Account of last viewed Mailbox'...
THIS is the kicker. (Randall Miller is officially a genius.) I screwed with this for a week and nothing else worked. Change the setting to Mail>Preferences>Composing>SEND NEW MAIL FROM ACCOUNT: Joe Smith <joesmith@verizon.net>
I'm not very tech-savvy (despite being a tech writer for 20 years), but my guess is that, when you have the setting at "Send New Mail from Account: Account of last view mailbox", Mail keeps the bad settings in some buffer and refers to them. Once you FORCE Mail to use the (corrected) outgoing server settings, it works every time. (Or at least this morning.)
That said, some of the other info presented above is wrong. (Sorry.) I have four mail accounts on three servers, and the settings vary wildly. Some servers require their name to be "mail.joesmith.com" and others just "joesmith.com". Some servers require the User Name as "joe" and some require "joe@joesmith.com".
Here are my Verizon settings that work (so far) after a week's fiddling.
In Mail>Preference>Accounts, I have:
Account type: POP
Description: Verizon
Email address: joe@verizon.net
Full name: Joe Smith
Incoming mail server: incoming.verizon.net
User name: joe
Password:
*** (the general verizon account password)
Mail server: outgoing.verizon.net (although this magically is rendered as outgoing.verizon.net:joe)
Server settings...
outgoing.verizon.net (no sign of the joe addition)
Server port: 25
Unchecked Use Secure Sockets Layer (SSL)
Authentication: Password
User name: joe
Password:
*** (general Verizon account password)
Added note: The Verizon Mac techie thought it was entirely due to a Keychain Access problem. Maybe. For good measure, I went into Keychain Access and deleted ALL my keychains. You might try that too. I can't tell if it's relevant.
I hope this helps.
Note Verizon is the WORST computer company I've seen in 20 years. Their website is a sprawling mess subdivided into fragments. There is no general logon password. Searches only search part of the site. There is very little tech help. If you send email to tech support, they send you a generic useless message. If you complain to billing, same reply. If you call on the phone, you'll be tracked not to help but to lists of MORE options and services to buy. It's even deceptive, such as "If you're having problems, you should try Verizon Encore", which is just another pay-for crap service. They have a robot to answer tech questions, and it's useless. If you can navigate the phone tree to tech support after 20 minutes, you'll get a Windows guy, who will then forward you to a Mac guy, another 20 minute wait, and he wasn't much help.
Verizon needs to get whacked with a class action suit. I switched to them from Comcast, which now runs dog-slow, but Verizon isn't much better.
Clayton Emery