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Spin-polarized vertical-cavity surface-emitting lasers (spin-VCSELs) and vertical external-cavity surface-emitting lasers (spin-VECSELs) are of interest since their output polarization can be manipulated by spin-selective pumping, either optical or electrical. These devices, using quantum dot (QD) material for the active region, have shown instability (periodic oscillations) and polarization switching in previous theoretical simulations based on a rate equation model. It has been recognized that the polarization switching occurs between two possible sets of solutions, termed here in-phase and out-of-phase. The present contribution seeks to give enhanced understanding of these behaviors by applying a stability analysis to the system of equations used for such simulations. The results indicate that the choice of in-phase and out-of-phase solutions that appear in a time-dependent simulation is determined by the condition that the corresponding steady-state solutions are stable against small perturbations. The stability analysis is shown to be a valuable theoretical tool for future study of spin-V(E)SELs in the context of understanding and guiding future experimental research.