Industrial prognosis refers to the prediction of failures of an industrial asset based on data collected by Internet of Things sensors. Prognostic models can experience the undesired effects of concept drift, namely, the presence of nonstationary phenomena that affects the data collected over time. Consequently, fault patterns learned from data become obsolete. To overcome this issue, contextual and operational changes must be detected and managed, triggering rapid model adaptation mechanisms. This article presents an adaptive learning approach based on a dendritic cell algorithm for drift detection and a deep neural network model that dynamically adapts to new operational conditions. A kernel density estimator with drift-based bandwidth is used to generate synthetic data for a faster adaptation, focusing on fine-tuning the lowest neural layers. Experimental results over a real-world industrial problem shed light on the outperforming behavior of the proposed approach when compared to other drift detectors and classification models.