The problem of the stability of planar channeling of high-energy positively charged particles in a crystal was studied on the basis of analytical calculation and numerical simulation. The evolution of the spectral density of radiation of particles with a decrease of the angle between particle momentum and atomic strings was investigated. The frequency of the peak in radiation, that corresponds to scattering by individual atomic strings in the case of planar channeling, was found. The analytical calculation was carried out in the parabolic planar potential approximation, while in the numerical simulation the Doyle-Turner approximation was used.