Recently, the outstanding performance reached by neural networks in many tasks has led to their deployment in autonomous systems, such as robots and vehicles. However, neural networks are not yet trustworthy, being prone to different types of misbehavior, such as anomalous samples, distribution shifts, adversarial attacks, and other threats. Furthermore, frameworks for accelerating the inference of neural networks typically run on rich operating systems that are less predictable in terms of timing behavior and present larger surfaces for cyber-attacks. To address these issues, this paper presents a software architecture for enhancing safety, security, and predictability levels of learning-based autonomous systems. It leverages two isolated execution domains, one dedicated to the execution of neural networks under a rich operating system, which is deemed not trustworthy, and one responsible for running safety-critical functions, possibly under a different operating system capable of handling real-time constraints. Both domains are hosted on the same computing platform and isolated through a type-1 real-time hypervisor enabling fast and predictable inter-domain communication to exchange real-time data. The two domains cooperate to provide a fail-safe mechanism based on a safety monitor, which oversees the state of the system and switches to a simpler but safer backup module, hosted in the safety-critical domain, whenever its behavior is considered untrustworthy. The effectiveness of the proposed architecture is illustrated by a set of experiments performed on two control systems: a Furuta pendulum and a rover. The results confirm the utility of the fall-back mechanism in preventing faults due to the learning component.