I actually think it's quite a random and mysterious process (who gets the 'stay an extra night' offer and who doesn't) - much like the equally mysterious 'who gets a special PIN code offer and who doesn't' subject. It probably largely depends on whether the hotel is booked or not, and if they have a lot of availability and can afford to let us have an extra day at a highly discounted rate, how many rooms they actually have available (because they might have to move you if you take the extra night), as well as what day of the week it is and if it is during a really busy holiday period or not. Also, the discounted amounts that they offer for the room are not always the same for everyone. They differ, and they might increase from year to year. One person might get a $109 offer for PPH, but the next time it might be $129.
I have gotten those 'stay an extra night' offers a few times and I have not been able to take advantage of them on any of those occasions, darn it!

I know I am forgetting about a couple of the occasions off the top of my head, but the two instances that come to mind right away were the time when I stayed at GCH for
one night only, on Thanksgiving weekend, and saw the offer in the envelope that was slipped under my door the next morning. I don't remember what the discounted amount was. The other time that I can recall off-hand was when I stayed at the PPH for 2 or 3 nights, and that 'extra night' offer was for
$99!!!!! (Believe me, I doubt I will ever get a $99 offer from the PPH again!)
Then, the one time I was finally ready and able to take advantage of an offer if I were to receive one (in December 2008), they didn't offer it to me!

One of the CMs at the GCH told me that they "never" make those 'stay an extra night' offers during holiday periods or really busy times.
One thing I have noticed is that, almost certainly, when my check-out bills have been attached to the outside of my door handle (to where I have to open the door to get the envelope), there is no offer for me. However, the envelopes that have included "the offer" were slid under the door. It's almost as if they wanted to make sure I saw the paperwork right away so I could decide if I wanted to take advantage of it or not - so they slid it under my door for me to see as soon as I woke up. When the envelope was hung on the outside of the door so that I couldn't see it, it was as if they hung it there because there wasn't anything they needed my response to right away and so it didn't matter if I saw the bill immediately or not!!

