Reconfigurable intelligent surfaces (RISs) have emerged as a promising technology to enhance the performance of sixth-generation (6G) and beyond communication systems. The passive nature of RISs and their large number of reflecting elements pose challenges to the channel estimation process. The associated complexity further escalates when the channel coefficients are fast-varying as in scenarios with user mobility. In this paper, we propose an extended channel estimation framework for RIS-assisted multiple-input multiple-output (MIMO) systems based on a convolutional neural network (CNN) integrated with an autoregressive (AR) predictor. The implemented framework is designed for identifying the aging pattern and predicting enhanced estimates of the wireless channels in correlated fast-fading environments. Insightful simulation results demonstrate that our proposed CNN-AR approach is robust to channel aging, exhibiting a high-precision estimation accuracy. The results also show that our approach can achieve high spectral efficiency and low pilot overhead compared to traditional methods.