This paper considers a wireless network where multiple flows are delivering status updates about their respective information sources. An end user aims to make accurate real-time estimations about the status of each information source using its received packets. As the accuracy of estimation is most impacted by events in the recent past, we propose to measure the credibility of an information flow by the number of timely deliveries in a window of the recent past, and say that a flow suffers from a loss-of-credibility (LoC) if this number is insufficient for the end user to make an accurate estimation. We then study the problem of minimizing the system-wide LoC in wireless networks where each flow has different requirement and link quality. We show that the problem of minimizing the system-wide LoC requires the control of temporal variance of timely deliveries for each flow. This feature makes our problem significantly different from other optimization problems that only involves the average of control variables. Surprisingly, we show that there exists a simple online scheduling algorithm that is near-optimal. Simulation results show that our proposed algorithm is significantly better than other state-of-the-art policies.