In this paper, we consider a status monitoring system where an energy harvesting sensor continuously sends time-stamped status updates to a destination. With a non-zero probability, each update will be corrupted by noise and result in an updating failure. The destination keeps track of the system status through the successfully delivered updates. We assume that there is a perfect feedback channel between the destination and the source, so that the source is aware of the updating failures once they occur. With the feedback information, our objective is to design the optimal online status updating policy to minimize the expected long-term average Age of Information (AoI) at the destination, subject to the energy causality constraint at the sensor. We propose a status updating policy called Best-effort Uniform updating with Retransmission (BUR), under which the source tries to equalize the delay between two successful updates as much as possible, and retransmits an update immediately if the previous transmission fails. We show that the BUR policy achieves the minimum expected long-term average AoI among a broad class of online policies.