I have requested two books that were available from two different senders.  Neither has accepted my request at this point but it seems that the date I requested as shown on the "details" section keeps changing to a more recent date, making it appear that I have requested each book only recently. What am I missing and it is highly possible that I am missing some important fact! :)  Thank you.

The requests are rolling over to another member.  Either they're timing out or senders are declining your request.

Here's the answer from the Help Center:

Why did the *Requested on:* date change on my request?

If the request date on a request you made has changed, that means the first sender did not complete the sending process by marking the book mailed to you, and your request has been automatically passed along to a new sender.

• Perhaps the first sender never responded at all
• Perhaps the first sender initally accepted your request, but never marked the book mailed
• Perhaps the first sender declined the request
• Perhaps the first sender declined your request because the book did not meet your Requestor Conditions
• Perhaps the first sender initially responded, but then canceled the transaction (if he or she couldn't find the book, for example)

If the transaction is not completed for any of these reasons, the PBS system will continue searching for a book until a copy is marked mailed to you (or until there are no other copies in the system, or until you cancel the request), all without any further effort from you.

If the date change is in the middle of the night, then that is the PBS system rolling the order over.  If the change was during the day, then it was a member deliberately marking that they could not fill the request.

You can add the book to your reminder list to see how many copies of the book are in the system.  Books with high numbers seem to roll over more often. 

Thanks, all.  I should have read more carefully. I guess I didn't think that there were other copies available of the books that I had requested. You answered my question.