In recent years, emerging research on mobile sensing has led to novel scenarios that enhance daily life for humans, but dynamic usage conditions often result in performance degradation when systems are deployed in real-world settings. Existing solutions typically employ one-off adaptation schemes based on neural networks, which struggle to ensure robustness against uncertain drifting conditions in human-centric sensing scenarios. In this paper, we propose CODA, a COst-efficient Domain Adaptation mechanism for mobile sensing that addresses real-time drifts from the data distribution perspective with active learning theory, ensuring cost-efficient adaptation directly on the device. By incorporating a clustering loss and importance-weighted active learning algorithm, CODA retains the relationship between different clusters during cost-effective instance-level updates, preserving meaningful structure within the data distribution. We also showcase its generalization by seamlessly integrating it with Neural Network-based solutions for Human Activity Recognition tasks. Through meticulous evaluations across diverse datasets, including phone-based, watch-based, and integrated sensor-based sensing tasks, we demonstrate the feasibility and potential of online adaptation with CODA. The promising results achieved by CODA, even without learnable parameters, also suggest the possibility of realizing unobtrusive adaptation through specific application designs with sufficient feedback.