Provided are a computer program product, system and method for managing Input/Output (I/O) requests to a storage device. In response to a write request, a determination is made as to whether preserve mode is enabled. A first entry is located in a volume control table for the logical address to write indicating a version number of the data and a first physical location in the storage device. The write data is written to a second physical location in the storage device. If the preserve mode is enabled, a second entry is added to the volume control table for the logical address, the volume control table is updated to have the first or second entry for the logical address point to the second physical location and indicate a current version, and the first or second entry not indicating the current version indicates the first physical location and a previous version.