An essential condition precedent to the success of mobile applications based on Wi-Fi (e. g., iCloud) is an energy-efficient Wi-Fi sensing. Clearly, a good Wi-Fi sensing policy should factor in both inter-access point (AP) arrival time (IAT) and contact duration time (CDT) distributions of each individual. However, prior work focuses on limited cases of those two distributions (e. g., exponential) or proposes heuristic approaches such as Additive Increase (AI). In this paper, we first formulate a generalized functional optimization problem on Wi-Fi sensing under general inter-AP and contact duration distributions and investigate how each individual should sense Wi-Fi APs to strike a good balance between energy efficiency and performance, which is in turn intricately linked with users mobility patterns. We then derive a generic optimal condition that sheds insights into the aging property, underpinning energy-aware Wi-Fi sensing polices. In harnessing our analytical findings and the implications thereof, we develop a new sensing algorithm, called Wi-Fi Sensing with AGing (WiSAG), and demonstrate that WiSAG outperforms the existing sensing algorithms up to 37% through extensive trace-driven simulations for which real mobility traces gathered from hundreds of smartphones is used.