Infrared dim and small target detection presents a significant challenge due to dynamic multi-frame scenarios and weak target signatures in the infrared modality. Traditional low-rank plus sparse models often fail to capture dynamic backgrounds and global spatial-temporal correlations, which results in background leakage or target loss. In this paper, we propose a novel motion-enhanced nonlocal similarity implicit neural representation (INR) framework to address these challenges. We first integrate motion estimation via optical flow to capture subtle target movements, and propose multi-frame fusion to enhance motion saliency. Second, we leverage nonlocal similarity to construct patch tensors with strong low-rank properties, and propose an innovative tensor decomposition-based INR model to represent the nonlocal patch tensor, effectively encoding both the nonlocal low-rankness and spatial-temporal correlations of background through continuous neural representations. An alternating direction method of multipliers is developed for the nonlocal INR model, which enjoys theoretical fixed-point convergence. Experimental results show that our approach robustly separates dim targets from complex infrared backgrounds, outperforming state-of-the-art methods in detection accuracy and robustness.