I have got it to do this twice so far, so looks like a problem. My wife always puts her X220 to sleep versus shutdown. Sleep still uses some power apparently which is fine. It looks like it is draining only the primary battery even though the slice battery is connected.
The issue is that with the primary battery drained and the slice battery connected, the TP will not power up. Plug the power adapter into the slice battery and still no power up. The slice battery charged to 100% with it pluged in, but the primary battery would not charge. Plug the power adapter into the X220 directly and let it charge for a moment, then everything works as it should even if you then move the power adapter back to the slice battery.
So if the primary battery is dead, the slice battery and charging the primary battery through it seems to stop working under this scenario.
Obviously not a huge deal since we now know what causes this, but maybe someone wants to fix some day.