Abstract. The North Atlantic subpolar gyre (SPG) plays a fundamental role in the Atlantic ocean circulation by providing an important connection between the subtropical Atlantic and the Arctic. It is driven by both wind and density differences that are, in part, caused by convection in the Labrador Sea. Through this deep convection site, the SPG is also linked to the AMOC. There is considerable evidence that this area of convection may diminish or shift in a changing climate. For this reason, the convection in the SPG is considered a tipping point. Here, we extensively study a conceptual model of the SPG to characterize the stability of convection in the gyre. The bifurcation structure of this model is analyzed in order to identify bistable parameter regions. For a range of gyre salinity and freshwater forcing levels the gyre is found to have both convective and non-convective states. Furthermore, noise-induced transitions between convective and non-convective states are possible for a wide range of parameter values. Convection in the SPG becomes increasingly unstable as the gyre salinity decreases and the freshwater forcing increases. However, convection never fully stops and can always restart after a period of no convection. This indicates that, at least in this conceptual model, a collapse of convection in the SPG does not have to be permanent.