Achieving fully autonomous embodied agents, particularly drones, in complex and dynamic real-world environments remains a significant challenge. While Large Language Models (LLMs) have advanced decision-making, existing systems struggle with extreme dynamic changes, instruction ambiguities, or complex failure modes requiring deeper scene understanding. Specifically, the efficiency of self-correction systems relies on intelligently filtering and distilling contextual information for LLMs to provide precise diagnostic evidence. This paper introduces ACR-Drone, an embodied drone autonomous task planning and self-iterative improvement system. ACR-Drone significantly enhances environmental comprehension and self-correction through an Adaptive Contextual Reasoning (ACR) mechanism. It integrates novel components such as dynamic semantic anchor points for initial Behavior Tree (BT) generation, an Adaptive Contextual Monitoring and Execution module featuring Context-Aware Filtering and Predictive State Reasoning, an Embodied Knowledge Base, and Hierarchical BT Refinement with Contextual Constraints for targeted modifications. Rigorous experimental validation, adhering to established task benchmarks, demonstrates that ACR-Drone consistently achieves superior overall task success rates, improved failure diagnosis, enhanced refinement efficiency, and greater robustness in both simulated and real-world environments, without requiring fine-tuning of the underlying LLMs. Our system's proactive detection capabilities and reduced refinement cycle times underscore the profound benefits of adaptive contextual reasoning for advanced drone autonomy.