Many current studies in tracking and surveillance assume that a target can be monitored by a single sensor. However, there are situations where a sensor can only monitor a certain portion of the object. Examples include image capturing and coastline monitoring. In our previous work, we develop the Minimum Cost Cover algorithm to identify a set of sensors which preserve 360° coverage of a target with minimum cost, such that when different cost functions for the sensors are used, covers with different optimization objectives can be identified. In this work, we study the scheduling problem to monitor a target continuously with full angle coverage. To increase network lifetime, we develop several algorithms by adopting different cost functions in selecting the sensors. We evaluate the performance of our schemes through extensive simulations. The simulation results show that our proposed Conditional Scheduling metric can help to improve the network lifetime as well as the time to the first node failure.