We exploit the accuracy of the reference hypernetted chain equation (RHNC) to study the stability of charged colloidal suspensions. To achieve this objective with confidence, we first check the performance of the RHNC integral equation by comparison with Gibbs ensemble Monte Carlo (GEMC) simulations for a simple DLVO potential. The results show that the theory describes accurately reversible coagulation into the secondary minimum for a typical intercolloidal potential. Once we have established this point, we make use of the theory to analyze the capability of the DLVO potential to describe appropriately certain experimental observations, in particular, the crossover from irreversible to reversible coagulation. In this regard we found that the inclusion of an empirical hydrophobic potential crucially affects the stability properties of the suspension and leads to an adequate prediction of the crossover diameter.