The evolution of the phase-space density profile in dark matter (DM) halos is investigated by means of constrained simulations, designed to control the merging history of a given DM halo. Halos evolve through a series of quiescent phases of a slow accretion intermitted by violent events of major mergers. In the quiescent phases the density of the halo closely follows the NFW profile and the phase-space density profile, Q(r) , is given by the Taylor & Navarro power law, r^−β, where β ≈ 1.9 and stays remarkably stable over the Hubble time. Expressing the phase-space density by the NFW parameters, Q(r) = Q_s(r/R_s)^−β, the evolution of Q is determined by Q_s. We have found that the effective mass surface density within R_s, Σ_s ≡ ρ_sR_s, remains constant throughout the evolution of a given DM halo along the main branch of its merging tree. This invariance entails that Q_s R_s^−5/2 and Q(r) Σ_s^−1/2R_s^−5/2(r/R_s)^−β. It follows that the phase-space density remains constant, in the sense of Q_s = const ., in the quiescent phases and it decreases as R_s^−5/2 in the violent ones. The physical origin of the NFW density profile and the phase-space density power law is still unknown. Yet, the numerical experiments show that halos recover these relations after the violent phases. The major mergers drive R_s to increase and Q_s to decrease discontinuously while keeping Q_s × R_s^5/2 = const . The virial equilibrium in the quiescent phases implies that a DM halos evolves along a sequence of NFW profiles with constant energy per unit volume (i.e., pressure) within R_s.