Brines are commonly found at depth in sedimentary basins. Many of these brines are known to be connate waters that have persisted since the early Paleozoic Era. Yet questions remain about their distribution and mechanisms for retention at depth in the Earth's crust. Here we demonstrate that there is insufficient topography to drive these dense fluids from the bottom of deep sedimentary basins. Our assessment based on driving force ratio indicates that sedimentary basins with driving force ratio > 1 contain connate waters and frequently host large evaporite deposits. These stagnant conditions appear to be relatively stable over geological time and insensitive to factors such as glaciations, erosion, compaction, and hydrocarbon generation.