Continuous monitoring of human physiology and behavior in natural environments via unobtrusively wearable wireless sensors is witnessing rapid adoption in both consumer health-care and in scientific studies, since those portable and long-running devices can provide critical information for diagnosis and early prevention of disease, as well as invaluable data for scientific studies. Due to the requirement of continuous monitoring, these sensors, all operating on small wearable batteries, require frequent recharging. Lowering this recharging burden is essential for their widespread adoption. In this paper we explore mechanisms for significantly enhancing the lifetime of these wearable sensors at the cost of a small loss in their sensing accuracy. We propose two ideas that build upon our observation that collecting bursts of samples over short periods of time is sufficient to capture the most interesting and informative part of the signal. In the first part of this paper, we propose a general methodology for reconstructing bandlimited signals accurately from such short bursts of samples. While this reconstruction task is in nature an ill-conditioned problem, we show that the insertion of an analog "modulated pre-filter" hardware module before the ADC can almost surely alleviate this conditioning problem. In the second part of this paper, we describe just-in-time sampling, which by sampling in short bursts at the "right" times, can accurately track R-wave peaks in ECG signals. Using simulations on publicly available traces as well as self-collected data, we show the efficacy of this technique.