The influence maximization (IM) problem involves identifying a set of key individuals in a social network who can maximize the spread of influence through their network connections. With the advent of geometric deep learning on graphs, great progress has been made towards better solutions for the IM problem. In this paper, we focus on the dynamic non-progressive IM problem, which considers the dynamic nature of real-world social networks and the special case where the influence diffusion is non-progressive, i.e., nodes can be activated multiple times. We first extend an existing diffusion model to capture the non-progressive influence propagation in dynamic social networks. We then propose the method, DNIMRL, which employs deep reinforcement learning and dynamic graph embedding to solve the dynamic non-progressive IM problem. In particular, we propose a novel algorithm that effectively leverages graph embedding to capture the temporal changes of dynamic networks and seamlessly integrates with deep reinforcement learning. The experiments, on different types of real-world social network datasets, demonstrate that our method outperforms state-of-the-art baselines.