The North Atlantic subpolar gyre is a counter-clockwise flowing ocean current that is partly driven by convection. There are indications that the convection in the subpolar gyre region can stop under climate change, with potentially large consequences for the wider North Atlantic. Here, we study a simple model of the subpolar gyre and find that in the scenarios we study, convection never stops permanently. This provides useful context for interpreting more complex models and observations.