We begin with the Wikipedia article which mentions that Li-ion batteries may die irreperably if they are discharged too far. (Also interesting to note that they don’t like being hot and are best stored at around 40% charge).
Then there’s the various posts about batteries dying at MacBookRandomShutdown, which is tracking 1828 people claiming to be affected by the problem. There’s the thread here, on Macintouch and Apple’s Discussion Forums.
Symptoms include a cross through the battery icon in the menu bar, and the message “No batteries available”. Interestingly one commenter mentions disassembling the battery pack and measuring the cell voltages, which seem fine. So it may be possible that the battery electronics themselves are crashing if the voltage gets too low, thus preventing the batteries from providing power.
So it seems there’s something wrong with MacBook batteries. Of course because of the problem the batteries are in short availability, and people are waiting 3 weeks or more for replacements, during which they can’t use their machines without plugging them in.