We propose Zygarde -- which is an energy -- and accuracy-aware soft real-time task scheduling framework for batteryless systems that flexibly execute deep learning tasks1 that are suitable for running on microcontrollers. The sporadic nature of harvested energy, resource constraints of the embedded platform, and the computational demand of deep neural networks (DNNs) pose a unique and challenging real-time scheduling problem for which no solutions have been proposed in the literature. We empirically study the problem and model the energy harvesting pattern as well as the trade-off between the accuracy and execution of a DNN. We develop an imprecise computing-based scheduling algorithm that improves the timeliness of DNN tasks on intermittently powered systems. We evaluate Zygarde using four standard datasets as well as by deploying it in six real-life applications involving audio and camera sensor systems. Results show that Zygarde decreases the execution time by up to 26% and schedules 9%-34% more tasks with up to 21% higher inference accuracy, compared to traditional schedulers such as the earliest deadline first (EDF).