In this work, we aim to explore and develop a speech analysis system that identifies relapses in patients with psychotic disorders (i.e., bipolar disorder and schizophrenia) with the long-term goal of monitoring and detecting relapse indicators, in order to aid in timely diagnoses of psychotic relapses. To this end, we utilize an unsupervised learning approach, employing convolutional autoencoders to build personalized speech models for patients. We use data from interviews between patients and clinicians to train and evaluate our models. The models are trained, learning to reconstruct spectrograms of speech segments corresponding to non-relapsing periods; then, the reconstruction error of the model is used to determine whether unseen speech data correspond to an anomalous (relapsing or pre-relapsing) state, or a stable one. A preliminary study using data from 5 patients and 95 interviews in total yielded encouraging results, indicating the potential usability of such models in real-time health monitoring.