Interconnected systems are prone to propagation of disturbances, which can undermine their resilience to external perturbations. Propagation dynamics can clearly be affected by potential time delays in the underlying processes. We investigate how such delays influence the resilience of production networks facing disruption of supply. Interdependencies between economic agents are modeled using systems of Boolean delay equations (BDEs); doing so allows us to introduce heterogeneity in production delays and in inventories. Complex network topologies are considered that reproduce realistic economic features, including a network of networks. Perturbations that would otherwise vanish can, because of delay heterogeneity, amplify and lead to permanent disruptions. This phenomenon is enabled by the interactions between short cyclic structures. Difference in delays between two interacting, and otherwise resilient, structures can in turn lead to loss of synchronization in damage propagation and thus prevent recovery. Finally, this study also shows that BDEs on complex networks can lead to metastable relaxation oscillations, which are damped out in one part of a network while moving on to another part.