Desert dust accounts for a substantial fraction of the total atmospheric aerosol loading. It produces important impacts on the Earth system due to its nutrient content and interactions with radiation and clouds. However, current climate models greatly underestimate its airborne lifetime and transport. For instance, super coarse Saharan dust particles (with diameters greater than $10\,\mathrm{\mu m}$) have repeatedly been detected in the Americas, but models fail to reproduce their transatlantic transport. In this study, we investigated the extent to which vertical turbulent mixing in the Saharan Air Layer (SAL) is capable of delaying particle deposition. We developed a theory based on the solution to a one-dimensional dust mass balance and validated our results using large-eddy simulation (LES) of a turbulent shear layer. We found that eddy motion can increase the lifetime of suspended particles by up to a factor of $2$ when compared with laminar flows. Moreover, we found that the increase in lifetime can be reliably estimated solely as a function of the particle Peclet number (the ratio of the mixing timescale to the settling timescale). By considering both the effects of turbulent mixing and dust asphericity, we explained to a large extent the presence of super coarse Saharan dust in the Caribbean observed during the SALTRACE field campaign. The theory for the lifetime of coarse particles in turbulent flows developed in this study is also expected to be applicable in other similar geophysical problems, such as phytoplankton sinking in the ocean mixed layer.