The behaviors and reflections of Alfred, the complexity of human behavior in general, and possible surrounding socioeconomic factors in "All the Years of Her Life" could lead a reader to reasonably make either conclusion about whether or not Alfred will steal again.
From reading the text, one could reasonably assume that Alfred and his family are not wealthy people and perhaps would be considered financially poor. One could infer this because Alfred's father works nights, which is often a position working-class people are put in; Alfred's mother does not drive at night to come to the drugstore but must walk; the narrator explains that Alfred's parents would be okay if only Alfred could keep a job; and Alfred, even though he has a job, explains that he is stealing so that he can have some money to spend with his friends. Financial factors, then, could certainly contribute to Alfred's future decision-making.
When patterns or habits are developed, they can be difficult to change, especially if there are no significant driving factors for change. Alfred certainly appears very afraid of the consequences of stealing, and that fear could motivate him to decide against stealing again in the future. Perhaps after his ordeal of being caught in the drugstore, and the acute fear that Alfred feels as a result, he will decide against stealing again.
Alfred's newfound respect and empathy for his mother may also be a significant factor in Alfred deciding not to steal again. He has seen his mother grieve his and his family's decisions before and has continued his pattern of getting into trouble, but on this particular night of the drugstore incident, he seems to see his mother in a new light. He is in awe of her, and as he watches her drink her tea alone in the kitchen with a "frightened, broken face," he feels a deep sense of empathy for her feelings and the struggles she has been through because of his actions. He sees now how his behavior has aged her, and as watches his mother, he feels he has also aged. This newfound respect and empathy for his mother may be the most significant driving factor in Alfred possibly deciding to commit to new patterns of behavior.