Dusty cirrus clouds are optically thick, convectively organized ice clouds that occur during intense mineral dust outbreaks. Previous modeling studies have found a link between mineral dust and convectively generated cirrus, but have been unable to explicitly resolve the associated convective dynamics due to limited spatial resolution. Here, we investigate the evolution and persistence of dusty cirrus using large-eddy simulations constrained by in-situ aircraft observations from the ML-CIRRUS 2014 campaign and complementary remote sensing data.<br />The simulations indicate that sustained convective cirrus requires mineral dust concentrations exceeding climatological values by approximately one to two orders of magnitude, corresponding to number concentrations on the order of N_d&sim; 1 cm^-3. Under these conditions, heterogeneous freezing on mineral dust dominates ice formation and maintains sufficiently high ice crystal number concentrations to sustain strong longwave cooling at cloud top and preserve convective overturning under shortwave radiative warming. In contrast, homogeneous freezing remains largely suppressed across a wide range of simulated conditions. The direct radiative effect of mineral dust is comparatively weak relative to cloud radiative feedbacks and does not significantly influence cirrus evolution.<br />The simulated cirrus is also highly sensitive to the choice of deposition ice nucleation parameterization, highlighting a major source of uncertainty in representing dust&ndash;ice interactions. Overall, the results identify mineral dust availability as the primary control on dusty cirrus persistence and emphasize the need for improved representation of heterogeneous ice nucleation in atmospheric models.