Numerical simulation of granular systems is often based on a discrete element method. The nonsmooth contact dynamics approach can be used to solve a broad range of granular problems, especially involving rigid bodies. However, difficulties could be encountered and hamper successful completion of some simulations. The slow convergence of the nonsmooth solver may sometimes be attributed to an ill-conditioned system, but the convergence may also fail. The prime aim of the present study was to identify situations that hamper the consistency of the mathematical problem to solve. Some simple granular systems were investigated in detail while reviewing and applying the related theoretical results. A practical alternative is briefly analyzed and tested.