We report on a long-term optical monitoring of the neutron star X-ray binary Centaurus X-4 performed during the last 13.5 yr. This source has been in quiescence since its outburst in 1979. Our monitoring reveals the overall evolution of the accretion disk; we detect short-duration flares, likely originating also in the disk, superimposed with a small-amplitude (<0.1 mag) ellipsoidal modulation from the companion star due to geometrical effects. A long-term (~2300 days) downward trend, followed by a shorter (~1000 days) upward one, is observed in the disk light curve. Such a rise in the optical has been observed for other X-ray binaries preceding outbursts, as predicted by the disk instability model. For Cen X-4, the rise of the optical flux proceeded for ~3 yr, and culminated in a flux increase at all wavelengths (optical-UV-X-rays) at the end of 2020. This increase faded after ~2 weeks, without giving rise to a full outburst. We suggest that the propagation of an inside-out heating front was ignited due to a partial ionization of hydrogen in the inner disk. The propagation might have stalled soon after the ignition due to the increasing surface density in the disk that the front encountered while propagating outward. The stall was likely eased by the low-level irradiation of the outer regions of the large accretion disk, as shown by the slope of the optical/X-ray correlation, suggesting that irradiation does not play a strong role in the optical, compared to other sources of emission.