So, whilst trying to finish one of Elizabeth's interminable requests, I stopped at the top of the stairs between levels to check a FAQ. Got distracted, and as it happens if you fart about on one level too long, Death himself shows up to give you a ding about the head. Which had happened by the time I got back to the game.
...apparently Death can't attack you on the stairs. He's stuck at the bottom and can't follow you up the whole three steps you can go before you have to switch levels.