Many organisms lose the capacity to regenerate damaged tissues as they mature. Damaged Drosophila imaginal discs regenerate efficiently early in the third larval instar (L3) but progressively lose this ability. This correlates with reduced damage-responsive expression of multiple genes, including the WNT genes wingless (wg) and Wnt6. We demonstrate that damage-responsive expression of both genes requires a bipartite enhancer whose activity declines during L3. Within this enhancer, a damage-responsive module stays active throughout L3, while an adjacent silencing element nucleates increasing levels of epigenetic silencing restricted to this enhancer. Cas9-mediated deletion of the silencing element alleviates WNT repression, but is, in itself, insufficient to promote regeneration. However, directing Myc expression to the blastema overcomes repression of multiple genes, including wg, and restores cellular responses necessary for regeneration. Localized epigenetic silencing of damage-responsive enhancers can therefore restrict regenerative capacity in maturing organisms without compromising gene functions regulated by developmental signals.