Emerging Low Earth Orbit (LEO) satellite networks, represented by Starlink, have developed a rapidly growing user base and increasing network traffic. Accurate and reliable satellite traffic prediction is essential for optimizing network performance and resource management. However, the high-speed motion of satellites and the uneven geographic distribution of users pose significant challenges to satellite network traffic prediction. Yet, empowered by Artificial Intelligence (AI) and inter-satellite links (ISLs), new opportunities arise. This article proposes a Real-time Resilient Traffic Prediction (RRTP) framework via adjacent satellite collaboration. Unlike existing methods that rely solely on historical data and delayed ground updates, by exchanging real-time traffic data, the onboard collaborative prediction learns the spatiotemporal traffic correlations among adjacent satellites, updates the parameters of the neural network models, and timely corrects the predicted traffic volume. The base model can be pre-trained on the ground and uploaded to satellites to save computations. Since RRTP requires neither global nor continuous long-term data exchange, RRTP enhances resilience to abrupt traffic changes and unexpected events, such as link/satellite failures. The overhead, cost, and applicability of RRTP are further discussed and validated through comparative simulations of a series of mega-constellation case studies.