I am continuing to work with Apple Tech Support. In the last 8 days I've had 1 telephone conversation and over 20 emails back and forth with the same person who is overseeing this reported problem for me. Last thing we did was two days ago, upload my entire address book to a new "test" iCloud account. Those birthdays have still not appeared. What also interesting is that a couple of the birthdays that I did get up into the iCloud's Birthday Calendar, have still not disappeared from the calendar. Basically, in my opinion, the calendar has not refershed in over 50 hours.
peterfromlaguna niguel: your tests regarding modifying birthdays is interesting. I've previously directed my Apple Tech Support contact to this forum, and I will do so again, pointing out your test conclusions.
The last email from Apple Tech Support person in part read as follows:
"I'm going to work with my engineers on this a little more and see what else we can come up with. ... I'll will be in contact as soon as I receive any updated information from my engineers."
Clearly, iCloud Birthday Calendar is not working right, at least for some. I'm glad that Apple is looking into this for me/us. As I've mentioned, please continue to report these problems to Apple. I believe if they get enough people reporting the problem, this will get figured out and fixed.