In this paper, the problem of continuity of the stability margin of a control system on problem input data is addressed. The case in which perturbations are linearly correlated is considered. It is shown that the existence of special points (called critical points) in the stability boundary manifold in parameter space plays a key role in the analysis of the problem. Several conditions, either sufficient or both necessary and sufficient, are given, ensuring continuity of the stability margin on problem data. The obtained conditions turn out to be easily checkable for practical applications. Numerical examples are presented to illustrate the proposed techniques.