We present the first unsupervised learning model for Maximum-Independent-Set (MaxIS) in dynamic graphs where edges change over time. Our method combines structural learning from graph neural networks (GNNs) with a learned distributed update mechanism that, given an edge addition or deletion event, modifies nodes' internal memories and infers their MaxIS membership in a single, parallel step. We evaluate our model against a mixed integer programming solver and a breadth of unsupervised and supervised learning models for combinatorial optimization on static graphs. Across dynamic graphs of 200-1,000 nodes, our model achieves approximation ratios that are competitive with the state-of-the-art models while running 1.91-6.70x faster. When generalizing to graphs with 100x more nodes than those used for training, our model produces MaxIS solutions 1.00-1.18x larger than all other unsupervised models, but is outperformed by the state-of-the-art supervised model. These results demonstrate that this novel, unsupervised, update-based learning approach to dynamic combinatorial optimization is a viable alternative to the naïve reapplication of analogous models for static graphs, leveraging temporal information to improve neural methods for combinatorial optimization.