Using galaxy clusters from the ESO Distant Cluster Survey, we study how the distribution of galaxies along the colour-magnitude relation has evolved since z~0.8. While red-sequence galaxies in all these clusters are well described by an old, passively evolving population, we confirm our previous finding of a significant evolution in their luminosity distribution as a function of redshift. When compared to galaxy clusters in the local Universe, the high redshift EDisCS clusters exhibit a significant "deficit" of faint red galaxies. Combining clusters in three different redshift bins, and defining as `faint' all galaxies in the range 0.4 > L/L* > 0.1, we find a clear decrease in the luminous-to-faint ratio of red galaxies from z~0.8 to z~0.4. The amount of such a decrease appears to be in qualitative agreement with predictions of a model where the blue bright galaxies that populate the colour-magnitude diagram of high redshift clusters, have their star formation suppressed by the hostile cluster environment. Although model results need to be interpreted with caution, our findings clearly indicate that the red-sequence population of high-redshift clusters does not contain all progenitors of nearby red-sequence cluster galaxies. A significant fraction of these must have moved onto the red-sequence below z~0.8.