The abandonment rate of patients who use CPAP devices for obstructive sleep apnea (OSA) therapy is as high as 60%. However, there is growing evidence that timely and appropriate intervention can improve long-term adherence to therapy. Current practice in sleep clinics of identifying potential patients who will abandon the treatment is not sufficiently effective in terms of accuracy and timeliness. Recent proposals in the literature have tried to identify non-adherent patients in a specific period of their therapy; however, there is no generalized approach by which clinical providers can monitor their patients continually with the goal of maximizing adherence. Towards this more generic goal, we propose CTAP-CPAP, a Continuous Treatment Adherence Prediction framework. With CTAP-CPAP, we address the problem of generalizing the prediction for any day in the treatment, where a robust framework with multiple machine learning models is implemented to assist medical practitioners keep track of the patient risk of non-adherence. Aiming the parallel progress of both machine learning and health informatics fields, we complement the study with a transparent discussion on the machine learning techniques used to build CTAP-CPAP and our view of its operationalization in a sleep clinic.