The Low Earth orbit Remote Sensing (LRS) satellite network is envisioned as an essential component of bolstering space information applications, thus extending conventional ground information applications to the on-board space information applications. However, it inevitably faces grave challenges imposed by the dynamics of the satellite network's topology, by the intermittence of Inter-Satellite communication Links (ISLs) as well as by the mobility-induced satellite-access switching of mobile terminals. Hence, this is a very different networking landscape from that of the terrestrial Internet. Against these challenging problems, we propose a resilient networking architecture for LRS Satellite Networks (LRS-SNs), with special emphasis on their dynamic routing, resilient transmission and their intrinsic mobility. Specifically, path-quality aided and lifetime-aware dynamic routing is proposed for enhancing the routing against dynamic topology changes. Hop-by-hop data transmission is relied upon for providing transmission resilience against ISL intermittence. Furthermore, data caching is invoked for providing resilience against intermittent communications imposed by dynamic satellite access switching. We employ a semi-physical simulation platform for evaluating the achievable performance of the proposed resilient network architecture.