Learning new tasks accumulatively without forgetting remains a critical challenge in continual learning. Generative experience replay addresses this challenge by synthesizing pseudo-data points for past learned tasks and later replaying them for concurrent training along with the new tasks' data. Generative replay is the best strategy for continual learning under a strict class-incremental setting when certain constraints need to be met: (i) constant model size, (ii) no pre-training dataset, and (iii) no memory buffer for storing past tasks' data. Inspired by the biological nervous system mechanisms, we introduce a time-aware regularization method to dynamically fine-tune the three training objective terms used for generative replay: supervised learning, latent regularization, and data reconstruction. Experimental results on major benchmarks indicate that our method pushes the limit of brain-inspired continual learners under such strict settings, improves memory retention, and increases the average performance over continually arriving tasks.