This appears to be a difference between AS6.1 and AS6.2. When I click the "Run without debugging" button in AS6.1 with the "Preserve EEPROM" project setting checked it works as I expect -- the EEPROM is preserved but the flash is reprogrammed. Using the exact same project/tool but opening it with AS6.2 the EEPROM is not preserved, and even more annoyingly, the EESAVE fuse on the device is then unchecked (not sure if the right term for fuses is 'cleared' or 'set' but it ends up in the state where EEPROM is not preserved.)
Is there a workaround for this? Some beta version of the Atmel Studio which fixes this bug maybe? It has really put a damper on my productivity.