We investigate the Lorentz structure of the confining potential through a study of the meson spectrum using Salpeter's instantaneous approximation to the Bethe-Salpeter equation. The equivalence between Salpeter's and a random-phase-approximation (RPA) equation enables one to employ the same techniques developed by Thouless, in his study of nuclear collective excitations, to test the stability of the solutions. The stability analysis reveals the existence of imaginary eigenvalues for a confining potential that transforms as a Lorentz scalar. Moreover, we argue that the instability persists even for very large values of the consitituent quark mass. In contrast, we find no evidence of imaginary eigenvalues for a timelike vector potential — even for very small values of the constituent mass.