I had the same problem. I found the following solution: on your Iphone go to "settings", "mail, contacts, calendars", then go to your primary Verizon account (or any account on your phone that is not receiving emails). When the screen for that comes up, go to "Advanced" at the bottom, then "Authentication". There should be a chckmark next to "Password". In my case this checkmark somehow was removed and caused the problem. If this is the case, hit "Password" and the checkmark will appear. Save the settings and close out of settings. When I did this, all my emails dumped into my inbox. Good luck.
Just off the phone with Verizon Tech. After upgrading from 4S to 6+ the reason I couldn't send emails was that the password needed to be put into two places. One for the out going mail and the other for the incoming mail. When your mail server asking you to put in the correct password it only updates the incoming password on the iphone and not the outgoing. Just go to >Settings>Mail, Contacts, Calendars>Verizon(what I called my mail account)>SMTP>smtp.verizon.net>Password and reenter your password
You would think the coder would have written code to do this for both incoming and outgoing servers; I get that some may use different passwords but I don't and serviously doubt anyone else would.