updated 02:46 pm EST, Wed February 5, 2014
Issue somehow linked to Bluetooth
Apple has issued a new support document, acknowledging a problem with AirPlay Mirroring freezing or dropping entirely. The issue appears to be limited to 2013 Mac Pro and MacBook Pro models, and only when connecting through an 802.11b/g Wi-Fi network. As a temporary solution, Apple notes that the problem can be fixed by turning off Bluetooth.
That answer may be problematic for Mac Pro owners, since the computer has no integrated input of its own, and buyers are more likely to be using wireless rather than wired mice and keyboards. Apple could conceivably fix the bug in OS X 10.9.2, but might choose to release separate patches to deal with it in the interim.