Degradation processes in industrial systems are notably difficult to monitor due to their hidden, evolving nature and complex nonlinear dynamics, posing significant challenges for accurate system modelling. Reconstruction errors of generative models have been used in literature to capture degradation dynamics; however, these models fail to fully exploit the representations in latent space, often resulting in overgeneralisation and making them ineffective at detecting subtle yet critical degradation patterns. To overcome these limitations, we present a novel system modelling framework, VAE-Enhanced Degradation-Aware System Identification (VDASI), that incorporates constrained latent spaces by integrating Variational Autoencoders (VAE) with Gaussian Process Nonlinear AutoRegressive models with Exogenous Inputs (GP-NARX). The framework operates in two distinct phases: the first captures degradation dynamics by employing reconstruction errors from both the original input space and constrained latent space, generating a reliable Degradation Index, while the second models key process variables. Results demonstrate the capability of VDASI, to outperform conventional approaches across five industrial datasets. By incorporating re-encoding layers and carefully constrained latent space, our approach increases sensitivity to dynamic degradation while avoiding overgeneralisation. This work underscores the critical role of well-constrained latent spaces in effectively capturing evolving degradation phenomena, and the importance of degradation-aware models in system identification.