I can't set the date on my new citizen's eco drive BM8080-59A. I don't know if I'm doing it wrong or if the date setting function is broken. I have tried to change the date by pulling the winder to the mid-level.

Yes that is ok its right by pulling the crown winder in the mid level or half level,that is for calendar date.To check if function is ok or broken,just pull full the crown and set the time,see if the calendar date is changing or moving.Then if moving then its ok,the next step you do set is the calendar date,by pulling the crown half pull,then turn the crown counterclockwise for date and for the day turn clockwise.Feel free to post whatever the result of the setting...

Hope it may helps you;

Regards,
VOTIT