A Power-Saving Mechanism (PSM) operates with sleep-mode and wake-mode, based on the receipt of requests for transition to each mode. The sleep-mode operation is manipulated by adjusting operating parameters such as the minimum sleep interval (T(min)) and the maximum sleep interval (T(max)). Interestingly, both energy consumption and the response delay of the request for a BS initiation of awakening are reciprocally affected by the relative sizes of these two operating parameters compared to the sleep duration (from the beginning of sleep-mode to that of wake-mode). To resolve this issue, this paper proposes a new PSM, called EPSM, which adaptively and simultaneously controls the operating parameters by efficiently reflecting the sleep duration. Moreover, depending on the current remaining energy state, this mechanism can also increase the available sizes of the operating parameters to be manipulated for achieving more intensive energy conservation. A numerical model is developed with a Markov chain for performance evaluation of the proposed mechanism pertaining to energy consumption and the response delay. The evaluation results substantiate that this mechanism can enhance energy conservation within reasonable response delay compared to the standard mechanism. Moreover, under an insufficient remaining energy state, the EPSM can prolong battery life while enduring an increasing response delay.