Living crystallization-driven self-assembly in solution has proven to be an excellent method to prepare core-crystalline micelles with an exquisite control over their size and morphology. While numerous studies have been performed to test their assembly in various media for potential applications, their stability under different stimuli remains yet to be established. In the present study, we performed light scattering and transmission electron microscopy experiments to investigate the effect of concentration on the self-seeding of core-crystalline one-dimensional (1D) seed crystallites with a long corona forming block. As previously reported, the seed crystallites dissolve much easier at low concentrations than at relatively high concentrations. We also observe that for all concentrations, the micelle width broadens during annealing. To explain these results, we developed a model based on a scaling approach. We show that the growth of ribbon-like core-crystalline micelles depends on the distance between the corona chains grafted on the micelle core, the thickness of the core, and, more surprisingly, on the number of chains constituting the core. This scaling approach also allowed us to explain how the interactions between the corona-forming block and the solvent influence the behavior of the seed crystallites at different annealing temperatures and concentrations. This model should thus prove very useful to understand and predict the effect of different media and stimuli on the size, morphology, and stability of core-crystalline micelles.