Context. 55 Cnc e is an ultra-short period super-Earth transiting a Sun-like star. Previous observations in the optical range detected a time-variable flux modulation that is phased with the planetary orbital period, whose amplitude is too large to be explained by reflected light and thermal emission alone. Aims. The goal of the study is to investigate the origin of the variability and timescale of the phase-curve modulation in 55 Cnc e. To this end, we used the CHaracterising ExOPlanet Satellite (CHEOPS), whose exquisite photometric precision provides an opportunity to characterise minute changes in the phase curve from one orbit to the next. Methods. CHEOPS observed 29 individual visits of 55 Cnc e between March 2020 and February 2022. Ba...