Detecting objects with visual sensors is crucial for numerous mobile robotics applications, from autonomous navigation to inspection. However, robots often need to operate under significant domains shifts from those they were trained in, requiring them to adjust to these changes. Tiny mobile robots, subject to size, power, and computational constraints, face even greater challenges when running and adapting detection models on low-resolution and noisy images. Such adaptability, though, is crucial for real-world deployment, where robots must operate effectively in dynamic and unpredictable settings. In this work, we introduce a new vision benchmark to evaluate lightweight continual learning strategies tailored to the unique characteristics of tiny robotic platforms. Our contributions include: (i) Tiny Robotics Object Detection~(TiROD), a challenging video dataset collected using the onboard camera of a small mobile robot, designed to test object detectors across various domains and classes; (ii) a comprehensive benchmark of several continual learning strategies on different scenarios using NanoDet, a lightweight, real-time object detector for resource-constrained devices.. Our results highlight some key challenges in developing robust and efficient continual learning strategies for object detectors in tiny robotics.es; (ii) a benchmark of different continual learning strategies on this dataset using NanoDet, a lightweight object detector. Our results highlight key challenges in developing robust and efficient continual learning strategies for object detectors in tiny robotics.