The protagonist in this excellent short story is so lonely because she does not fit in to her surroundings, either culturally or emotionally, and the love that caused her to enter these surroundings in the first place has not vanished, leaving her alone in a world that she does not comprehend and where she does not belong. Note how the protagonist describes her lost love and her current state:
Yes, I am sick--but not just for home. I am sick for a time, a time that was and that I can never have again. A lover I had and can never have again.
The protagonist is stranded in this alien environment to her as she desperately wishes for a return to the past but has to acknowledge that the past is never going to return for her. Her loneliness is embodied in the image of the sandpiper, a bird that is left on the fringes of the land, walking where the land and sea merge. The protagonist sees herself and her position in this bird as she is left on the borders and is not able to enter the society where she lives.