git-bash.exe runs bash.exe via cmd.exe, which means the console (conhost.exe) ends up with 5 attached processes:

    cmd.exe
        bash.exe
            bash.exe
                py.exe
                    python.exe

The default console configuration uses 4 history buffers, so by the time python.exe runs, they've all been used up. You can change this in the Alt+Space control menu's "Properties" dialog. This should modify the settings associated with cmd.exe, which are stored at "HKCU\Console\%SystemRoot%_system32_cmd.exe". In the upper right section increase the number of buffers to 32. You can also increase the size. I increase it to 500 commands. Start a new console via "Git Bash Here" to confirm that the new settings are remembered.  

Also modify the default configuration used for new programs, which is stored at "HKCU\Console". Back on the Alt+Space control menu, choose "Defaults" and similarly modify the size and number of buffers. 

Note that if you run a console program using a shortcut, such as the default "Command Prompt" shortcut, the console configuration is stored in the .LNK shortcut file instead of the registry.