High dropout rates in psychotherapy, particularly in depression, remain a major clinical challenge and are further exacerbated in vulnerable populations such as hikikomori youth. Machine learning has emerged as a promising strategy to support treatment monitoring; however, applications in Internet-delivered Cognitive Behavioural Therapy (ICBT), especially for early dropout warning, remain limited. In this context, we propose a longitudinal, speech-driven early-warning framework to monitor dropout risk among hikikomori patients undergoing ICBT in a real-world clinical setting. Instead of treating dropout as a static classification endpoint, disengagement is modeled as a discrete-time forecasting problem, where binary supervision is used only to estimate longitudinal risk trajectories across sessions. Our framework integrates multimodal information—self-supervised speech representations, interpretable acoustic descriptors, and behavioral engagement indicators—within a GRU-based temporal architecture. Results indicate that multimodal modeling enhances sensitivity to early disengagement signals and enables clinically meaningful early-warning indicators, achieving a positive-class recall of 0.73 with specificity of 0.50, and detecting risk up to 2 sessions before dropout. These findings highlight the potential of longitudinal speech-based monitoring to support proactive clinical intervention and improve retention in digital psychotherapy.