There is definitely an element of wise caution in Eveline's decision to stay. Let us remember that there is much uncertainty in the alternative future that she is trying to convince herself to embark upon, especially because of the way that she will be going to a completely foreign country where she knows nobody and will be a wife to a man that she doesn't know very well:
She was about to explore another life with Frank. Frank was very kind, manly, open-hearted. She was to go away with him by the night-boat to be his wife and to live with him in Buenos Aires where he had a home waiting for her.
She is on the point of exchanging everything she has ever known--her entire world--for a complete unknown, and so perhaps we can see an element of wise caution in her decision to stay.
However, when we look at the rest of the story, we can see that by far the stronger force that forces her to stay is that of duty and religion. In the face of these two forces, Eveline finds her self passive and unable to assert herself. Even though she clearly wants to leave and escape the future that awaits her, as the memory of her mother's death shows, when she finally reaches the harbour and the crucial moment, she is unable to actually move, and she returns to the same frozen, passive state in which she started the story, gripping the handrail and unable to move:
He rushed beyond the barrier and called to her to follow. He was shouted at to go on but he still called to her. She set her white face to him, passive, like a helpless animal. Her eyes gave him no sign of love or farewell or recognition.
It is above all this state of paralysis that she suffers that makes her decision for her, or, to be more accurate, takes the ability to make the decision from her.