Hybrid parallelism underpins large-scale LLM training across tens of thousands of GPUs. At such scale, hardware failures on individual devices lead to performance skew across devices, diminishing overall training efficiency. Existing resilient systems overlook sequence length variability in datasets and device performance skew under hybrid parallelism. As a result, (1) iteration time fluctuations induced by sequence length variability can trigger spurious fail-slow detections, and (2) failures are mitigated through individual adaptations in hybrid parallelism, leading to unnecessary detection overhead and inefficient resilient training. To respond, this paper presents ResiHP, a resilient system that enables robust failure detection and fine-grained adaptation for hybrid parallel training. First, we develop a Detector to accurately identify failures. In particular, it employs a workload-aware execution time predictor that disentangles failures from iteration time fluctuations while remaining lightweight for online detection. Second, we design a Scheduler that dynamically adapts parallelism group sizes, model partitioning, and workload scheduling policies to improve training efficiency under failures. Experiments show that ResiHP improves training throughput by 1.04-4.39$\times$ compared with state-of-the-art resilient training systems under diverse failure scenarios in a 256-GPU cluster.