A disk drive is disclosed including a disk comprising a plurality of refresh zones, and a head actuated over the disk. The disk drive further comprises control circuitry for receiving access commands from a host. The control circuitry refreshes a refresh zone in a plurality of segments with an interval between each segment, and processes at least one of the access commands during the interval between at least two of the segments, wherein a size of each segment and the interval ensures an average throughput of access commands received from the host does not fall below a first threshold.