Deploying object detection on microcontrollers (MCUs) enables intelligent edge devices but current models cannot learn new object categories after deployment. Existing continual learning methods require storing raw images far exceeding MCU memory budgets of tens of kilobytes. We present Latent Replay Detection (LRD), the first framework for continual object detection under MCU memory constraints. Our key contributions are: 1. Task-Adaptive Compression: Unlike fixed PCA, we propose learnable compression with FiLM (Feature-wise Linear Modulation) conditioning, where task specific embeddings modulate the compression to preserve discriminative features for each task's distribution; 2. Spatial-Diverse Exemplar Selection: Traditional sampling ignores spatial information critical for detection - we select exemplars maximizing bounding box diversity via farthest-point sampling in IoU space, preventing localization bias in replay; 3. MCU-Deployable System: Our latent replay stores 150 bytes per sample versus >10KB for images, enabling a 64KB buffer to hold 400+ exemplars. Experiments on CORe50 (50 classes, 5 tasks) demonstrate that LRD achieves mAP@50 on the initial task and maintains strong performance across subsequent tasks - a significant improvement over naive fine-tuning while operating within strict MCU constraints. Our task-adaptive FiLM compression and spatial diverse exemplar selection work synergistically to preserve detection capabilities. Deployed on STM32H753ZI, ESP32-S3, and MAX78000 MCUs, LRD achieves 4.9-97.5ms latency per inference within a 64KB memory budget-enabling practical continual detection on edge devices for the first time.