Satellite networks are able to collect massive space information with advanced remote sensing technologies, which is essential for real-time applications such as natural disaster monitoring. However, traditional centralized processing by the ground server incurs a severe timeliness issue caused by the transmission bottleneck of raw data. To this end, Space Computing Power Networks (Space-CPN) emerges as a promising architecture to coordinate the computing capability of satellites and enable on board data processing. Nevertheless, due to the natural limitations of solar panels, satellite power system is difficult to meet the energy requirements for ever-increasing intelligent computation tasks of artificial neural networks. To tackle this issue, we propose to employ spiking neural networks (SNNs), which is supported by the neuromorphic computing architecture, for on-board data processing. The extreme sparsity in its computation enables a high energy efficiency. Furthermore, to achieve effective training of these on-board models, we put forward a decentralized neuromorphic learning framework, where a communication-efficient inter-plane model aggregation method is developed with the inspiration from RelaySum. We provide a theoretical analysis to characterize the convergence behavior of the proposed algorithm, which reveals a network diameter related convergence speed. We then formulate a minimum diameter spanning tree problem on the inter-plane connectivity topology and solve it to further improve the learning performance. Extensive experiments are conducted to evaluate the superiority of the proposed method over benchmarks.