Structural health monitoring (SHM) is vital for ensuring the safety and longevity of structures like buildings and bridges. As the volume and scale of structures and the impact of their failure continue to grow, there is a dire need for SHM techniques that are scalable, inexpensive, operate passively without human intervention, and customized for each mechanical structure without the need for complex baseline models. We present a novel "deploy-and-forget" approach for automated detection and localization of damages in structures. It is based on a synergistic combination of fully passive measurements from inexpensive sensors and a mechanics-informed autoencoder. Once deployed, our solution continuously learns and adapts a bespoke baseline model for each structure, learning from its undamaged state's response characteristics. After learning from just 3 hours of data, it can autonomously detect and localize different types of unforeseen damage. Results from numerical simulations and experiments indicate that incorporating the mechanical characteristics into the variational autoencoder allows for up to 35\% earlier detection and localization of damage over a standard autoencoder. Our approach holds substantial promise for a significant reduction in human intervention and inspection costs and enables proactive and preventive maintenance strategies, thus extending the lifespan, reliability, and sustainability of civil infrastructures.