The correct representation of the Maud Rise open‐ocean polynya in the Weddell Sea remains a challenge for ocean models. Here we reproduce the most recent polynya openings in 2016–2017 using a regional configuration, and assess their dependencies on vertical convective mixing schemes and freshwater forcing, both separately and in combination. We test three vertical convective mixing schemes: the enhanced vertical diffusion (EVD), the Eddy‐Diffusivity Mass‐Flux (EDMF) parameterization, and a modified version of EDMF accounting for thermobaric effects. Using simulations for the period 2007–2017, we find that the modified EDMF reproduces the observed climatological evolution of the mixed layer depth better than the original EDMF and the EVD, but a polynya fails to open due to excessive freshwater forcing. We thus use the modified EDMF to perform sensitivity experiments with reduced precipitation during 2012–2017. The imposed freshwater forcing strongly affects the number of years with polynyas. The simulation with the best representation of the 2016–2017 polynyas is analyzed to evaluate the triggering mechanisms. The 2016 polynya was induced by the action of thermobaric instabilities on a weak ambient stratification. This opening preconditioned the water column for 2017, which produced a stronger polynya. By examining the impacts of the different convective mixing schemes, we show that the modified EDMF generates more realistic patterns of deep convection. Our results highlight the importance of surface freshwater forcing and thermobaricity in governing deep convection around Maud Rise, and the need to represent thermobaric instabilities to realistically model Maud Rise polynyas. Plain Language Summary We investigate the impacts of representing numerical vertical mixing and surface freshwater forcing in a regional ocean model on polynyas (large openings in the pack ice) at Maud Rise, Southern Ocean. Maud Rise is prone to hosting polynyas, often associated with deep convection, which is a local vertical mixing process homogenizing the water column between surface and depths of several hundred meters. Numerical models often use simplistic strategies to represent this process, but improved parameterizations have recently become available. In this work, we test the impact of the representation of convective mixing in a particularly sensitive region. The last Maud Rise polynyas were observed in 2016 and 2017. Our regional simulation is capable of reproducing these polynyas, which has long been a challenge for ocean‐sea ice models. We show that the 2016 polynya resulted from the action of a vertical instability at depth acting on weak ambient stratification. This event preconditioned the stronger 2017 polynya and deep convection. We conclude that representing convective plumes as a sub‐grid scale process in models leads to a more realistic representation of open‐ocean polynyas and associated convection events. Key Points The Eddy‐Diffusivity Mass‐Flux (EDMF) parameterization is tested in a regional simulation of the ocean around Maud Rise Thermobaric effects on convective plumes are enabled by modifying the EDMF parameterization Simulations of Maud Rise polynyas are highly sensitive to freshwater forcing and mixing schemes