Steppers are very inefficient and generally, horrible for battery operated devices.
For the stepper to maintain position, in most cases you need to keep it powered all the time, making it nearly impossible to get decent battery life.
So, for the moment, forget the "sleep" option, and concentrate on the electromechanical part.
With the high gear ratio of the 28BJY motor, you might be able to turn it off and not lose position. But verify that first.