Chances are you are using a large amount of current and that's why your batteries are running out fast. A 9v battery can run 500mA for roughly an hour. I would figure out how much current you are using and look for a battery that can supply that for the amount of time you are expecting it to run for.
It seems the unit consumes 90 mA with the LCD background light switched off. Uhm, it seems a high consumption. That's why the battery is running out fast. Do you think is it possible to connect the unit directly to the 12 volts battery?
I think then I should consider to use a solar power to charge the 12 volts battery...