EEG-based mobile monitoring is recognized to be a resource-constrained activity because of the limited mobile battery, the intermittent network, and the size of EEG signal generated from continuous monitoring. In this paper, we propose a novel approach combining both EEG compression and mobile resource availability evaluation to boost and save energy for longer monitoring episode. The main core of our approach lies in developing and implementing an algorithm, which evaluates on the fly the compression cost and available resources on the mobile device to decide whether to fully/partially compress the input EEG data or not. We experimentally evaluated and tested the effectiveness of our approach using both offline and online data recorded by the Emotiv EEG device. The obtained results show that our approach significantly saves mobile battery and processing power to cope with critical health situations.