An evidence that the dielectric aging in the polydomain Pb(Zr0.45Ti0.55)O-3 thin films is controlled by progressive pinning of 180 degrees domain walls is presented. To provide such a conclusion, we use a general method, which is based on the study of the time evolution of the nonlinear but anhysteretic dielectric response of the ferroelectric to a weak electric field. A thermodynamic model of the ferroelectric system where the dielectric response is controlled by bending movements of pinned 180 degrees domain walls is developed. Within this model, the nonlinear permittivity of the ferroelectric is expressed as a function of the microstructural parameters of the domain pattern. It is shown that by using the analysis of the time evolution of the nonlinear permittivity, it is possible to estimate changes in the concentration of the pinning centers that block the movements of the 180 degrees domain walls during aging in polydomain perovskite ferroelectrics.