A technique automatically handles a failure during online data migration from a source array to a target array. While a host initially accesses data from the source array using multipath I/O software, the technique involves (i) transitioning the source array to a passive mode, and the target array to an active mode, and (ii) beginning a data transfer operation which transfers data from the source array to the target array. The technique further involves modifying the data on both the target array and the source array in response to modification commands sent to the target array from the host while the data transfer operation is ongoing. The technique further involves automatically failing back to providing access to the data from the source array in response to an event in which the target array loses communication with the source array for a predefined amount of time.