There was no room at the PEK transit hotel
I showed up at the hourly lounge with the hotel-like rooms in the public area of the arrival level at PEK Terminal 3 at about 11 pm on February 12, 2010. And, unfortunately, despite assurances (obtained by two Chinese friends who called the facility to inquire on my behalf about the reservation policy and availability norms) that rooms "were almost always available", there was no room. Per advice on this thread, I asked about availability at hourly lounges at other terminals, and the lady shook her head "no".
Long story short, I ended up staying at the "flea bag" 1-star Hang Lu Airport Hotel, a representative of which was lingering outside the transit hotel to recruit prospective customers like me who were being turned away from the transit hotel. The rate was 380 RMB. It was a pretty sad place, with some customers checking out at midnight while I was checking in (an observation leading to an obvious conclusion as to the typical purpose of the hotel). But they did have a free shuttle van to/from the airport, and I was able to get a few hours' sleep.
But a lesson learned here: I will no longer rely on availability at any lodging facility, including airport transit hotels, that does not accept reservations.
And if you want to "rough it" sleeping at the Beijing airport, there are some reclining chairs just outside the McDonalds (which is all the way to the left as you exit the baggage claim into the public part of the arrival level). The next morning, I met a couple from Finland who took that action. It had been cold inside the airport overnight and they said they were ill-equipped to deal with the cold, as they were en route home from Thailand (not sure how they would deal with the cold upon arriving home in Finland).