The transition to extreme edge inference, facilitated by Artificial Intelligence of Things (AIoT), has unlocked unprecedented opportunities for real-time inspection of technical facilities with battery-operated sensors equipped with resourced-constrained processors. Besides, the quality of the monitoring process largely depends on the sensing parameters, i.e., the sampling frequency and the acquisition duration, which impact in opposite manner on the diagnostic performance and the energy autonomy. In this work, we evaluate this trade-off when profiled on a low-cost and self-contained acceleration sensor suited for AIoT vibration-based installations, considering the KW51 bridge dataset as target application case. As a major contribution, the proposed analysis unveils the non-trivial balance between the different phases involved in the damage detection process. Counterintuitively, systems based on commercial microprocessors—lacking advanced power-gating strategies—benefit from relatively high sampling frequencies, being the sampling duration the dominant factor affecting both accuracy and energy requirements, significantly limiting the role played by the inference stage.