We analyze the stability of super- and subradiant states in a system of identical two-level atoms in the near-Dicke limit, i.e., when the atoms are very close to each other compared to the wavelength of resonant light. The dynamics of the system are studied using a renormalized master equation, both with multipolar and minimal-coupling interaction schemes. We show that both models lead to the same result and, in contrast to unrenormalized models, predict that the relative orientation of the (co-aligned) dipoles is unimportant in the Dicke limit. Our master equation is of relevance to any system of dipole-coupled two-level atoms, and gives bounds on the strength of the dipole-dipole interaction for closely spaced atoms. Exact calculations for small atom systems in the near-Dicke limit show the increased emission times resulting from the evolution generated by the strong dipole-dipole interaction. However, for large numbers of atoms in the near-Dicke limit, it is shown that as the number of atoms increases, the effect of the dipole-dipole interaction on collective emission is reduced.