In traditional computing systems, software problems are often resolved by platform restarts. This approach, however, cannot be naïvely used in cyber-physical systems (CPS). In fact, in this class of systems, ensuring safety strictly depends on the ability to respect hard real-time constraints. Several adaptations of the Simplex architecture have been proposed to guarantee safety in spite of misbehaving software components. However, the problem of performing recovery into a fully operational state has not been extensively addressed. In this work, we discuss how resets can be used in CPS as an effective strategy to recover from a variety of software faults. Our work extends the Simplex architecture in a number of directions. First, we provide sufficient conditions under which safety is guaranteed in spite of fault-induced resets. Second, we introduce a novel technique to express not only state-dependent safety constraints, as typically done in Simplex, but also time-dependent safety properties. Finally, through a proof-of-concept minimal implementation on a small R/C helicopter and simulation-based system modeling, we show the effectiveness of the proposed recovery strategy under the assumed fault model.