<p>In this paper, we investigate parametric nonconvex polynomial optimization problems in which the noncompact convex feasible set is defined by finitely many convex polynomial inequalities. We introduce a regularity condition to study the stability of such problems and compare it with existing assumptions in the literature. Under suitable conditions, we provide a detailed characterization of stability properties for polynomial optimization problems. In particular, we establish sufficient conditions for the upper semicontinuity of the solution map, necessary and sufficient conditions for its lower semicontinuity, as well as sufficient conditions for the upper and lower semicontinuity of the optimal value function. We also derive necessary and sufficient conditions for the continuity of the optimal value function and for the lower semicontinuity of the local solution map. In the main results, both the objective function and the constraint set are subject to perturbations. Furthermore, illustrative examples are presented to clarify and support the theoretical findings. Finally, we extend our results to more general classes of polynomial optimization problems.</p>