Nuclei instance segmentation in pathological images is crucial for downstream tasks such as tumor microenvironment analysis. However, the high cost and scarcity of annotated data limit the applicability of fully supervised methods, while existing semi-supervised methods fail to adequately regularize consistency at the instance level, lack leverage of the inherent prior knowledge of pathological structures, and are prone to introducing noisy pseudo-labels during training. In this paper, we propose an Instance-Aware Robust Consistency Regularization Network (IRCR-Net) for accurate instance-level nuclei segmentation. Specifically, we introduce the Matching-Driven Instance-Aware Consistency (MIAC) and Prior-Driven Instance-Aware Consistency (PIAC) mechanisms to refine the nuclei instance segmentation result of the teacher and student subnetwork, particularly for densely distributed and overlapping nuclei. We incorporate morphological prior knowledge of nuclei in pathological images and utilize these priors to assess the quality of pseudo-labels generated from unlabeled data. Low-quality pseudo-labels are discarded, while high-quality predictions are enhanced to reduce pseudo-label noise and benefit the network's robust training. Experimental results demonstrate that the proposed method significantly enhances semi-supervised nuclei instance segmentation performance across multiple public datasets compared to existing approaches, even surpassing fully supervised methods in some scenarios.