While generalist robot policies hold significant promise for learning diverse manipulation skills through imitation, their performance is often hindered by the long-tail distribution of training demonstrations. Policies learned on such data, which is heavily skewed towards a few data-rich head tasks, frequently exhibit poor generalization when confronted with the vast number of data-scarce tail tasks. In this work, we conduct a comprehensive analysis of the pervasive long-tail challenge inherent in policy learning. Our analysis begins by demonstrating the inefficacy of conventional long-tail learning strategies (e.g., re-sampling) for improving the policy's performance on tail tasks. We then uncover the underlying mechanism for this failure, revealing that data scarcity on tail tasks directly impairs the policy's spatial reasoning capability. To overcome this, we introduce Approaching-Phase Augmentation (APA), a simple yet effective scheme that transfers knowledge from data-rich head tasks to data-scarce tail tasks without requiring external demonstrations. Extensive experiments in both simulation and real-world manipulation tasks demonstrate the effectiveness of APA. Our code and demos are publicly available at: https://mldxy.github.io/Project-VLA-long-tail/.