Satellite-ground semantic communication is anticipated to serve a critical role in the forthcoming 6G era. Nonetheless, task-oriented data transmission in such systems remains a formidable challenge, primarily due to the dynamic nature of signal-to-noise ratio (SNR) fluctuations and the stringent bandwidth limitations inherent to low Earth orbit (LEO) satellite channels. In response to these constraints, we propose an importance-aware robust semantic transmission (IRST) framework, specifically designed for scenarios characterized by bandwidth scarcity and channel variability. The IRST scheme begins by applying a segmentation model enhancement algorithm to improve the granularity and accuracy of semantic segmentation. Subsequently, a task-driven semantic selection method is employed to prioritize the transmission of semantically vital content based on real-time channel state information. Furthermore, the framework incorporates a stack-based, SNR-aware channel codec capable of executing adaptive channel coding in alignment with SNR variations. Comparative evaluations across diverse operating conditions demonstrate the superior performance and resilience of the IRST model relative to existing benchmarks.