A shutdown of ocean convection in the subpolar North Atlantic, triggered by enhanced melting over Greenland, is regarded as a potential transition point into a fundamentally different climate regime1,2,3. Noting that a key uncertainty for future convection resides in the relative importance of melting in summer and atmospheric forcing in winter, we investigate the extent to which summer conditions constrain convection with a comprehensive dataset, including hydrographic records that are over a decade in length from the convection regions. We find that warm and fresh summers, characterized by increased sea surface temperatures, freshwater concentrations and melting, are accompanied by reduced heat and buoyancy losses in winter, which entail a longer persistence of the freshwater near the surface and contribute to delaying convection. By shortening the time span for the convective freshwater export, the identified seasonal dynamics introduce a potentially critical threshold that is crossed when substantial amounts of freshwater from one summer are carried over into the next and accumulate. Warm and fresh summers in the Irminger Sea are followed by particularly short convection periods. We estimate that in the winter 2010–2011, after the warmest and freshest Irminger Sea summer on our record, ~40% of the surface freshwater was retained.