The open radio access network (O-RAN) enables modular, intelligent, and programmable 5G network architectures through the adoption of software-defined networking (SDN), network function virtualization (NFV), and implementation of standardized open interfaces. It also facilitates closed loop control and (non/near) real-time optimization of radio access network (RAN) through the integration of non-real-time applications (rApps) and near-real-time applications (xApps). However, one of the security concerns for O-RAN that can severely undermine network performance and subject it to a prominent threat to the security & reliability of O-RAN networks is jamming attacks. To address this, we introduce SAJD-a self-adaptive jammer detection framework that autonomously detects jamming attacks in artificial intelligence (AI) / machine learning (ML)-integrated O-RAN environments. The SAJD framework forms a closed-loop system that includes near-real-time inference of radio signal jamming interference via our developed ML-based xApp, as well as continuous monitoring and retraining pipelines through rApps. Specifically, a labeler rApp is developed that uses live telemetry (i.e., KPIs) to detect model drift, triggers unsupervised data labeling, executes model training/retraining using the integrated & open-source ClearML framework, and updates deployed models on the fly, without service disruption. Experiments on O-RAN-compliant testbed demonstrate that the SAJD framework outperforms state-of-the-art (offline-trained with manual labels) jamming detection approach in accuracy and adaptability under various dynamic and previously unseen interference scenarios.