Convolutional Neural Networks (CNNs) pre-trained on large-scale datasets such as ImageNet are widely used as feature extractors to construct high-accuracy classification models from scarce data for specific tasks. In such scenarios, fine-tuning the pre-trained CNN is difficult due to data scarcity, necessitating the use of fixed weights. However, when the weights are kept fixed, many filters that do not contribute to the target task remain in the model, leading to unnecessary redundancy and reduced efficiency. Therefore, effective methods are needed to reduce model size by pruning filters that are unnecessary for inference. To address this, approaches utilizing Layer-wise Relevance Propagation (LRP) have been proposed. LRP quantifies the contribution of each filter to the inference result, enabling the pruning of filters with low relevance. However, existing LRP-based pruning methods have been observed to cause cascading accuracy degradation. In this study, we introduce an accuracy-aware pruning control mechanism for existing LRP-based filter pruning methods, which suppresses cascading accuracy degradation by dynamically adjusting the pruning rate and the pruning order using the harmonic mean of class accuracy, and compresses the pre-trained model while preserving task-specific performance in a small-data environment. We demonstrate that this control mechanism effectively mitigates cascading accuracy degradation and achieves higher classification accuracy compared to existing LRP-based pruning methods, improving the class-averaged area under the accuracy-pruning-rate curve (AUC) of VGG16 by approximately 15\% over conventional LRP-based approaches.