I spoke with Apple's iCloud support folks over the weekend. Apparently, we have exceeded a time-based password reset requirement. The support engineer could not quantify the time period. He said it was something new that he had not encountered previously. My password was also years old, so who knows?
I explained to him the problem in not only having to change the password, but also the website did not specify what the problem was or that a password change requirement was being imposed.
He apologized for this, agreed it was not very and asked that I also make note of my concerns on the Customer Feedback page: http://www.apple.com/feedback page
So, I went through the headache of changing my password.
At any rate, I wanted to give you all an explanation that went beyond posting a link to Apple Support.