Advancements in the \Internet of Things (IoT)" concept enables large numbers of low-power wireless sensors and electronic devices to be connected to the Internet and outside world over a wide area wireless network without a need for human interaction. Using rechargeable batteries with energy harvesting to power these wireless sensors has been shown to preserve the self-sustainability and selfsu fficiency of a sensor node and prolong its lifetime, hence the whole network it belongs to. However, it brings the question of how to intelligently manage the energy in the battery so that the node maintains its functionalities by keeping the battery level over zero for an extended duration of time, known as the lifehorizon. We propose a risk-theoretic Markov uid queue model to compute the battery outage probability of a wireless sensor node for a given finite life-horizon. The proposed method enables the performance evaluation of a wide spectrum of energy management policies including those with adaptive sensing rate (or duty cycling). In this model, the node gathers data from the environment according to a Poisson process whose rate is to depend on the instantaneous battery level and/or the state of the energy harvesting process (EHP) which is characterized by a Continuous time Markov Chain (CTMC). Moreover, an engineering methodology is proposed by which optimal threshold-based adaptive sensing rate policies are obtained that maximize the information sensing rate of the sensor node while meeting lifetime constraints given in terms of battery outage probabilities. Numerical results are presented for the validation of the analytical model and also the proposed engineering methodology, using two-state CTMC-based EHPs.