Is it normal to love when theres no hope

i feel in love with an alcoholic girlfriend,and she said how much she loved me,but she would always leave me,she said to go drink but i would find her in bars talking to guys,i don't know if she cheated she said she never did,18 to 20 times she would leave and say she was at her sisters but not answer the phone,but i could not stop loving her,she had me and she new it then i told her if she left i would to,and i did i moved away we talked and she said she would not drink,like so many times before,and i would believe her,she came home with marks like hickies and say they were bruises,well it would last a month then she would go out,now its been ten days and no word,and i cant stop loving her,please help i don't want to hurt no more