We study the thermodynamic stability of the Kerr-AdS black hole from the perturbative corrections to the gravitational partition function. The line of critical stability is identified by the appearance of a negative mode of the Euclidean action that renders the partition function ill-defined. The eigenvalue problem, consisting of a system of three coupled partial differential equations for the metric perturbations, is solved numerically. The agreement with the standard condition of thermodynamic stability in the grand canonical ensemble is remarkable. The results illustrate the physical significance of gravitational partition functions for rotating spacetimes beyond the instanton approximation.