Semantic segmentation networks are usually pre-trained and not updated during deployment. As a consequence, misclassifications commonly occur if the distribution of the training data deviates from the one encountered during the robot's operation. We propose to mitigate this problem by adapting the neural network to the robot's environment during deployment, without any need for external supervision. Leveraging complementary data representations, we generate a supervision signal, by probabilistically accumulating consecutive 2D semantic predictions in a volumetric 3D map. We then retrain the network on renderings of the accumulated semantic map, effectively resolving ambiguities and enforcing multi-view consistency through the 3D representation. To preserve the previously-learned knowledge while performing network adaptation, we employ a continual learning strategy based on experience replay. Through extensive experimental evaluation, we show successful adaptation to real-world indoor scenes both on the ScanNet dataset and on in-house data recorded with an RGB-D sensor. Our method increases the segmentation performance on average by 11.8% compared to the fixed pre-trained neural network, while effectively retaining knowledge from the pre-training dataset.