As future M2M (Machine-to-Machine) communications aim at supporting wireless networks which feature long range, long operating duration and large device number, the IEEE 802.11ah Task Group is going to specify a global WLAN standard that utilizes carrier frequencies below 1GHz. To power the M2M devices, harvesting energy from ambient environment has attracted attentions from researchers. Although applying the IEEE 802.11 PSM (Power-Saving Mode) scheme reduces energy consumption, devices go to sleep only when the traffic buffer is empty, staying awake unnecessarily, which wastes energy in overhearing the uplink traffic transmitted to the AP. In this paper, we propose DeepSleep, a novel energy-aware scheme, which grants higher channel access priority for low energy level devices dynamically. Moreover, applying DeepSleep scheme alleviates the channel congestion by randomly deferring the wake up time of the devices, thereby achieving higher energy-efficiency, which saves nearly 75 % of energy per delivered packet. Additionally, the overall performance improvement when DeepSleep devices co-exist with 802.11 devices is also verified.