A potentially irreversible threshold in Antarctic ice shelf melting would be crossed if the ocean cavity beneath the large Filchner–Ronne Ice Shelf were to become flooded with warm water from the deep ocean. Previous studies have identified this possibility, but there is great uncertainty as to how easily it could occur. Here, we show, using a coupled ice sheet-ocean model forced by climate change scenarios, that any increase in ice shelf melting is likely to be preceded by an extended period of reduced melting. Climate change weakens the circulation beneath the ice shelf, leading to colder water and reduced melting. Warm water begins to intrude into the cavity when global mean surface temperatures rise by approximately 7 °C above pre-industrial, which is unlikely to occur this century. However, this result should not be considered evidence that the region is unconditionally stable. Unless global temperatures plateau, increased melting will eventually prevail.