Precision experiments, such as the search for electric dipole moments of charged particles using radio-frequency spin rotators in storage rings, demand for maintaining the exact spin resonance condition for several thousand seconds. Synchrotron oscillations in the stored beam modulate the spin tune of off-central particles, moving it off the perfect resonance condition set for central particles on the reference orbit. Here, we report an analytic description of how synchrotron oscillations lead to non-exponential decoherence of the radio-frequency resonance driven up–down spin rotations. This non-exponential decoherence is shown to be accompanied by a nontrivial walk of the spin phase. We also comment on sensitivity of the decoherence rate to the harmonics of the radio-frequency spin rotator and a possibility to check predictions of decoherence-free magic energies.