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Door-status detection, namely recognizing the presence of a door and its status (open or closed), can induce a remarkable impact on a mobile robot's navigation performance, especially for dynamic settings where doors can enable or disable passages, changing the topology of the map. In this work, we address the problem of building a door-status detector module for a mobile robot operating in the same environment for a long time, thus observing the same set of doors from different points of view. First, we show how to improve the mainstream approach based on object detection by considering the constrained perception setup typical of a mobile robot. Hence, we devise a method to build a dataset of images taken from a robot's perspective and we exploit it to obtain a door-status detector based on deep learning. We then leverage the typical working conditions of a robot to qualify the model for boosting its performance in the working environment via fine-tuning with additional data. Our experimental analysis shows the effectiveness of this method with results obtained both in simulation and in the real-world, that also highlight a trade-off between costs and benefits of the fine-tuning approach.