Colloidal CdSe nanoplatelets with monolayer control over their thickness can now be synthesized in solution and display interesting optical properties. From a fundamental point of view, the self-assembly of CdSe nanoplatelets can impact their optical properties through short-range interactions, and achieving control over their dispersion state in solution is of major relevance. The related issue of colloidal stability is important from an applicative standpoint in the perspective of the processing of these materials. Using UV-vis spectroscopy, we assess the colloidal stability of dispersions of CdSe nanoplatelets at different nanoparticle and ligand (oleic acid) concentrations. We unravel an optimum in oleic acid concentration for colloidal stability and show that even moderately concentrated dispersions flocculate on a time scale ranging from minutes to hours. Small-angle X-ray scattering shows that the precipitation proceeds through a face-to-face stacking of the nanoplatelets due to long-ranged van der Waals attraction. To address this issue, we coated the platelets with a carboxylic acid-terminated polystyrene, thus achieving colloidal stability while retaining the optical properties of the platelets.