Given that wearable sensors that are attached on patients for the purpose of continuous real-time medical monitoring typically need to remain operational for periods of up to 24 hours before a battery change or recharge, power preservation schemes play a critical role in minimizing any possible disruption to a patient's daily activities. In this paper, we propose a motion-based wake-up scheme, a feature which combines motion detection with existing power preservation schemes in order to achieve a balance between energy saving and data timeliness, particularly in critical situations. As a showcase, we have integrated this feature with a healthcare application and demonstrate the capability of the scheme to deal with critical events, e.g., when a patient falls down from the bed. This showcase affirms the effective uses of our proposed motion-based wake-up scheme.