<p>The scarcity of labeled data in real-world applications has sparked interest in semi-supervised learning (SSL) methods. However, traditional SSL models often rely on assumptions like the manifold or low-density separation, which may not hold in dynamic streaming environments. This challenge is further exacerbated by concept drift and high dimensionality, which impairs the effectiveness of SSL models. In this paper, we introduce DMReSSL, a pioneering deep metric framework for reliable semi-supervised learning under concept drift. Unlike conventional approaches, DMReSSL leverages a metric learning module to transform the original data features into a metric latent space, where it dynamically maintains a set of metric-embedded micro-clusters with evolving reliability attributes. The reliability of these micro-clusters is updated in an online fashion, based on prediction performance, time effects, and local label distributions, ensuring that the model adapts to changing data distributions. Extensive experiments conducted on eight real-world and six synthetic datasets demonstrate that DMReSSL outperforms the second-best algorithm by 1.32% in accuracy using only 5% of labeled data, significantly enhancing model robustness and efficiency in semi-supervised data streams learning.</p>