In this article, we investigate an energy harvesting (EH) wireless sensor network for the Internet of Things (IoT) where monitoring applications require a continuous update of sensing information. The considered system consists of independent EH sensor nodes equipped with capacitors and providing, through unreliable channels, status updates to a non EH sink. The distribution of the interdelivery time, i.e., the time elapsed between two successive and successful status update deliveries, is derived in the closed-form expression considering a random EH arrival process. Moreover, the interdelivery violation probability metric, defined as the probability to exceed a predetermined interdelivery threshold, is analyzed. Our analysis reveals that the violation probability is highly dependent on the size of the capacitor. Both analytical and simulation results demonstrate the existence of an optimal capacitor size that achieves the minimum violation probability. Moreover, our findings reveal an interesting tradeoff in the system design. On one hand, a small capacitor charges quickly and thus status updates are sent more frequently but with lower transmit power and thus a high error rate. On the other hand, a large capacitor increases the transmit power and boosts the successful data transmission probability, at the expense of a higher waiting time before filling the capacitor and transmitting sensed data.