In this paper, a low-power high-response wireless structural health monitoring system (WSHMS) is designed, implemented and experimentally evaluated for impact detection in composite airframes. Due to the rare, random and transitory nature of impacts, an event-triggered mechanism is adopted for allowing the system to exhibit low power consumption when no impact occurs and high performance when triggered. System responsiveness, robustness and energy efficiency are considered and modelled. Based on system requirements and functions, several modules are designed, including filtering, impact detecting, local processing and wireless communicating modules. The system was implemented on a printed circuit board. The response time is about 12 us with an average current lower than 1 mA when the impact activity is lower than 0.1%. The system exhibits high robustness to ambient vibration noises and is also capable of accurately and responsively capturing multiple sensing input channels (up to 24 channels). This work presents a low-latency energy-aware WSHMS for impact detection of composite structures. It can be adapted to monitor of other rare, random and ephemeral events in many Internet of Things applications.