Your point is well taken. I use Yahoo and Hotmail. I also have a Gmail account which I don't care much for and never use. And, as it turns out, multiple accounts are what finally led me to the solution (I believe and hope) to this problem.
It kept bugging me that one of the error messages I kept getting was asking for me to enter a password for my hotmail account while the problem itself only appeared when I tried to access my Yahoo mail. This made no sense to me. And it was compounded by the other error message stating that my connection to the server had failed.
J.A. first mentioned it and it sorta stuck in the back of my mind. Thanks, J.A.
Since my Hotmail account has a separate icon on a home page that I've always used to access it, the question occurred to me as to why there was also a Hotmail account appearing in the list of accounts shown in Settings>Mail, Contacts, Calendars. I wondered what would happen if I deleted it. Would I lose my Hotmail account altogether? I decided to risk it since my Yahoo account is my principal email account.
After deleting it I went to my home page and clicked on the Hotmail icon and it opened normally. I then closed it and clicked on the mail icon at the bottom of the page where I've always accessed my Yahoo account. My Yahoo account then opened BUT THE PROBLEM WAS GONE. I spent the rest of the evening randomly checking to be sure it stayed gone but it hasn't returned. Thank goodness.
I don't know how or why there was a second access point for a Hotmail account but it must have had an incorrect password associated with it which prompted the request for a correct one. I can't guess what prompted the error message regarding a server failure but, at this point, I don't care. I'm just happy that the problem has been solved.
Many, many thanks to all of you who contributed your time and expertise toward solving this PITA. You're great folks and I very much appreciate your help.
Have a beautiful, glorious day.....