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Transfer learning has become a dominant paradigm for addressing the persistent small-data limitation in computational materials science, particularly through pre-training graph neural networks on large-scale repositories and subsequent fine-tuning on task-specific datasets. This strategy assumes that universal atomic-scale representations—such as local coordination environments, bonding characteristics, and elemental embeddings—transfer effectively across domains. However, accumulating empirical evidence reveals a systematic and reproducible failure: in small-data regimes, fine-tuned models frequently underperform both zero-shot pre-trained models and models trained from scratch. This work presents a comprehensive failure-mode analysis demonstrating that such collapse is not incidental but structurally inevitable under common conditions in materials applications. Four interdependent mechanisms are identified—catastrophic forgetting, negative transfer, representation distortion, and overfitting amplification—arising from irreducible source–target domain mismatch, feature entanglement in equivariant graph architectures, and the statistical insufficiency of target datasets typically containing fewer than 10³ samples. Under these constraints, the corrective signal provided by target data is inadequate to overcome entrenched source biases or to reconfigure internal representations. Drawing exclusively on consolidated literature, we show that transfer learning failure emerges when domain similarity falls below critical thresholds and when data scarcity prevents stable optimization. The study further formalizes operational diagnostics—including baseline benchmarking, source-validation tracking, and learning-rate sensitivity analysis—and introduces mitigation strategies such as progressive unfreezing, elastic weight consolidation, replay-based regularization, and similarity-gated transfer decisions. By reframing transfer learning as a high-risk, condition-dependent strategy rather than a default solution, this work provides a principled foundation for robust model deployment in materials informatics. It challenges prevailing assumptions of universal transferability and advocates for systematic failure-mode reporting to ensure reliability in machine-learned interatomic potentials and property prediction workflows.