Welcome to Justanswer.com, my name is Dustin.I'm sorry to hear about the issue you are having, I will do my best to help you resolve it.
The simplest and most reliable way I know of to ensure you can check your email hassle free, is to use the Verizon app itself, rather then the phones built in email app. Since you have had the same issues on three phones, im sure youre looking for a more permanent solution then a temporary settings fix to the email app.
So Id try the my verizon / my fios app here that will allow you to check your email using the app.. this app always works unless your account was hacked or you changed your password ( and didnt update the app with the new password )
This is a simple, effective, and long term solution.. If after installing and using the app to check your email you decide this isnt a solution you want to continue using, let me know and we can go through the process of repairing the email problem so you can continue using the stock email app until the next verizon service issue breaks the app / account again.
I strive to provide great service, and greatly appreciate a 5 star rating clicked and submitted when you are satisfied.. I always answer follow up questions.Dustin S.Senior Technician and Network Switching Systems Operator / Maintainer.