The forthcoming sixth-generation (6G) mobile network is set to merge edge artificial intelligence (AI) and integrated sensing and communication (ISAC) extensively, giving rise to the new paradigm of edge intelligent sensing (EI-Sense). This paradigm leverages ubiquitous edge devices for environmental sensing and deploys AI algorithms at edge servers to interpret the observations via remote inference on wirelessly uploaded features. A significant challenge arises in designing EI-Sense systems for 6G mission-critical applications, which demand high performance under stringent latency constraints. To tackle this challenge, we focus on the end-to-end (E2E) performance of EI-Sense and characterize a source-channel tradeoff that balances source distortion and channel reliability. In this work, we establish a theoretical foundation for the source-channel tradeoff by quantifying the effects of source coding on feature discriminant gains and channel reliability on packet loss. Building on this foundation, we design the coding rate control by optimizing the tradeoff to minimize the E2E sensing error probability, leading to a low-complexity algorithm for ultra-low-latency EI-Sense. Finally, we validate our theoretical analysis and proposed coding rate control algorithm through extensive experiments on both synthetic and real datasets, demonstrating the sensing performance gain of our approach with respect to traditional reliability-centric methods.