From the document you posted:
"The steel containment vessel provides the heat transfer surface that removes heat from inside
the containment and rejects it to the atmosphere. Heat is removed from the containment vessel
by continuous natural circulation flow of air. During an accident, the air cooling is supplemented
by evaporation of water. The water drains by gravity from a tank located on top of the
containment shield building.
Calculations have shown the AP1000 to have a significantly reduced large release frequency
following a severe accident core damage scenario. With only the normal PCS air cooling, the
containment stays well below the predicted failure pressure for at least 24 hours. Other factors
include improved containment isolation and reduced potential for LOCAs outside of
containment. This improved containment performance supports the technical basis for
simplification of offsite emergency planning." .......
"Long-term accident mitigation - A major safety advantage of the AP1000 versus current-day
PWRs is that long-term accident mitigation is maintained by the passive safety systems without
operator action and without reliance on offsite or onsite ac power sources. For the limiting
design basis accidents, the core coolant inventory in the containment for recirculation cooling
and boration of the core is sufficient to last for at least 30 days, even if inventory is lost at the
design basis containment leak rate." ......
Where does that document say things go to hell after 3 days if the coolant is not topped up? It seems to me that 60 MW of heat could easily be removed via natural convection over the large surface area of the steel containment vessel.