Okay, without doing anything (except sending that test email) my iPhone local mail account is now working. I did reinstall the account on my iPad2. It took forever as it did not want to authenticate the account. Repeatedly timed out. But, finally, it worked and now that mail account is receiving and sending mail.
If I read the notes correctly, one item that 8.2 addresses is Mail. I have no idea why this account was rejected by both devices suddenly, after working with no hesitation for a long time. I am just as confounded as to why the iPhone suddenly then started to work with no corrective action on my part. That both devices now recognize the mail account is good, of course.