In energy-harvesting sensor networks, limited ambient energy from environment necessitates sensor nodes to operate at a low-duty-cycle, i.e., they communicate briefly and stay asleep most of time. Such low-duty-cycle operation leads to orders of magnitude longer communication delays in comparison with traditional always-active networks, imposing a new challenge in many time-sensitive sensor network applications (e.g., tracking and alert). In this paper, we introduce novel solutions for bounding sink-to-node communications in energy-harvesting sensor networks. We first present an optimal solution for the sink-to-one case and its distributed implementation. For the sink-to-many case, we theoretically prove its NP-Hardness and inapproximability property, followed by an efficient heuristic solution.We have evaluated our design with both extensive simulation and a TinyOS/Mote based implementation. Compared with an improved version of a state-of-the-art design, our delay maintenance design effectively provides E2E delay guarantees while consuming as much as 60% less energy.