Background: The COVID-19 pandemic has highlighted the need for robust diagnostic tools capable of detecting the disease from diverse and evolving data sources. Machine learning models, especially convolutional neural networks (CNNs), have shown promise. However, the dynamic nature of real-world data can lead to model drift, where performance degrades over time as the underlying data distribution changes. Addressing this challenge is crucial to maintaining accuracy and reliability in diagnostic applications. Objective: This study aims to develop a framework that monitors model drift and employs adaptation mechanisms to mitigate performance fluctuations in COVID-19 detection models trained on dynamic audio data. Methods: Two crowd-sourced COVID-19 audio datasets, COVID-19 Sounds and COSWARA, were used. Each was divided into development and post-development periods. A baseline CNN model was trained and evaluated using cough recordings from the development period. Maximum mean discrepancy (MMD) was used to detect changes in data distributions and model performance between periods. Upon detecting drift, retraining was triggered to update the baseline model. Two adaptation approaches were compared: unsupervised domain adaptation (UDA) and active learning (AL). Results: UDA improved balanced accuracy by up to 22% and 24% for the COVID-19 Sounds and COSWARA datasets, respectively. AL yielded even greater improvements, with increases of up to 30% and 60%, respectively. Conclusions: The proposed framework addresses model drift in COVID-19 detection, enabling continuous adaptation to evolving data. This approach ensures sustained model performance, contributing to robust diagnostic tools for COVID-19 and potentially other infectious diseases.