If air circulation failed completely later on, the oxygen supply would deplete but I expect the pressure wouldn't drop suddenly. The engines would still try to pump in air, blocking that avenue, while the exhaust valve would try to keep pressure up and close.

737 pilots interviewed in the wake of the crash also strongly point to possible empty O<inf>2</inf> cannisters as the reason the cockpit crew was incapacitated.

Starting to look messy...