Recently, a large number of low Earth orbit (LEO) satellites have been launched and deployed successfully in space. These LEO satellites are equipped with advanced multimodal sensors capable of collecting massive sensor data, serving as fuel for various space-based deep learning (DL) applications. However, ground stations (GS) cannot download such massive raw data for centralized training due to intermittent connectivity between satellites and GS, while the scaled-up DL models pose substantial barriers to distributed training on resource-constrained satellites. Though split learning (SL) has emerged as a promising solution to offload major training workloads to GS via model partitioning, the reliance on continuous connectivity significantly limits its deployment in satellite networks. To address this challenge, we propose ESL-LEO, an efficient SL framework specifically tailored for LEO satellite networks to enable full-satellite period training. We first construct an auxiliary model to tackle the training failure of the satellite-GS non-contact time, leveraging on-satellite idle resources to expedite model convergence. Moreover, we design the online knowledge distillation mechanism to extract GS-side knowledge for guiding and refining the satellite-side training, thereby further enhancing training performance. Extensive experiments demonstrate that ESL-LEO outperforms state-of-the-art benchmarks in both accuracy and convergence speed.