The firmware instructions state the following:

" Updating the Intelligent Flight Battery Firmware

The Intelligent Battery is upgraded during the aircraft firmware process."


Does this mean that we need to refresh the firmware update for each new battery that we install ?


When they finally become available.
                                       
                                
                        
               

Yes - there is firmware in the smart batteries for the Inspire 1, P2V+ and the new P3.  It is not updated with every new firmware release, but if the battery firmware is updated, it is included in the same firmware bin file as is used to update the firmware of the P3 and it updates the battery firmware at the same time.  If you have multiple batteries, you would power down after doing one battery, check for the txt file with SUCCESS message, delete that txt file from the SD card, put it back in the P3 gimbal SD card slot, install the next battery, and power on the P3 again.  This time it would only update the new battery firmware.

According to the "How to upgrade" pdf, the battery update is done during the aircraft update but it is done after a power cycle ?!!! The same if I was saying "it is black but it is white"
So in fact nobody even at DJI knows how to do ?

The Intelligent Flight Battery is upgraded during the aircraft firmware upgrade process. It is recommended to keep the upgrade package files in your SD card. The upgrade will start automatically after power cycling the aircraft.