During deployment, an object detector is expected to operate at a similar performance level reported on its testing dataset. However, when deployed onboard mobile robots that operate under varying and complex environmental conditions, the detector's performance can fluctuate and occasionally degrade severely without warning. Undetected, this can lead the robot to take unsafe and risky actions based on low-quality and unreliable object detections. We address this problem and introduce a cascaded neural network that monitors the performance of the object detector by predicting the quality of its mean average precision (mAP) on a sliding window of the input frames. The proposed cascaded network exploits the internal features from the deep neural network of the object detector. We evaluate our proposed approach using different combinations of autonomous driving datasets and object detectors.