Like tissues of many organisms, Drosophila imaginal discs lose the ability to regenerate as they mature. This loss of regenerative capacity coincides with reduced damage-responsive expression of multiple genes needed for regeneration. We previously showed that two such genes, wg and Wnt6, are regulated by a single damage-responsive enhancer that becomes progressively inactivated via Polycomb-mediated silencing as discs mature (Harris et al., 2016). Here we explore the generality of this mechanism and identify additional damage-responsive, maturity-silenced (DRMS) enhancers, some near genes known to be required for regeneration such as Mmp1, and others near genes that we now show function in regeneration. Using a novel GAL4-independent ablation system we characterize two DRMS-associated genes, apontic (apt), which curtails regeneration and CG9752/asperous (aspr), which promotes it. This mechanism of suppressing regeneration by silencing damage-responsive enhancers at multiple loci can be partially overcome by reducing activity of the chromatin regulator extra sex combs (esc).