The time series of normalized difference vegetation index (NDVI) and interferometric coherence extracted from optical and Synthetic Aperture Radar (SAR) images, respectively, have strong responses to sudden landslide failures in vegetated regions, which is expressed by a sudden increase or decrease in the values of NDVI and coherence. Compared with optical sensors, SAR sensors are not affected by cloud and daylight conditions and can detect the occurrence time of failure in near real-time. The purpose of this paper is to automatically determine the time of failure occurrence using time series coherence values. We propose, based on some existing anomaly detection algorithms, a deep neural network-based anomaly detection strategy that combines supervised and unsupervised learning without a priori knowledge about failure time. Our experiment using July 21, 2020 Shaziba landslide in China shows that in comparison to widely used unsupervised methodology, the use of our algorithm leads to a more accurate detection of the timing of the landslide failure.