What are Eveline´s reasons for staying in Dublin in james Joyce's "Eveline"?
Eveline doesn't really have reasons for staying in Dublin and for permitting Frank to go without her to Buenos Ayres. "Reasons" implies, in fact is defined as, a process of judgement that ascertains a basis for and a cause for actions or beliefs, etc. Having reasons for something strongly suggests a successful process of rational thought and committment to a resultant conviction.
The night before the ship embarked for Buenos Ayres Eveline succeeded in using rational judgement (to an extent) and chose a reason for an action and made a committment to a conviction: she agreed to go with Frank as is proven by her presence on the dock. From then on, however, Eveline is motivated--more like undone--by confused, abused religious notions of duty ("she prayed to God to direct her, to show her what was her duty") that have gone astray through the affects and influences of mistreatment, guilt, sorrow, grief, unhappiness, fear, confusion.
It is these things that make Eveline freeze in immobility of mind, soul, volition, and personality as she clings in confusion to her confusion ("Her distress awoke a nausea in her body,...All the seas of the world tumbled about her heart...") which is symbolized by the rail, as she looks blankly at Frank: "passive, like a helpless animal. Her eyes gave him no sign of...recognition."
Duty and paralysis are two of the major themes of James Joyce's Dubliners, and the eponymous character in "Eveline" suffers from both when she is incapable of leaving Dublin to Buenos Ayres.
The vast majority of the story occurs with Eveline sitting at her window, looking out at the streets of her childhood and noticing how things have changed—the neighborhood, her family, her relationship with her father. Throughout the story, Joyce employs free indirect discourse, delving into the mind of Eveline and revealing that she keeps thinking about the promise she made her mother to "to keep the home together as long as she could." Near the end of the story, she recalls the last thing her mother told her: "Derevaun Seraun," Gaelic for "at the end of pleasure, is pain." These two memories in which Eveline feels duty-bound to her family, especially to her dead mother, effectively paralyze Eveline and prevent her from boarding the ship with Frank.