This is a great question! My own belief is that the postmaster does not have adequate coping skills.
The postmaster lacks effective coping skills in a couple of ways. The first is how he is incapable of making good out of a bad situation. He does not demonstrate much in the way of toughness while he is in Ulapur. While he does try his hand at writing, most of his time is spent regretting being there. He does not interact with the people who live there and sees the village in a manner that is either arrogant or confused. This reflects one aspect of his inability to effectively deal with something difficult.
The postmaster is used to being coddled. When the postmaster is sick, Tagore brings out this aspect of his character: "He wished his mother or sister were sitting here next to him, soothing his illness and loneliness with feminine tenderness." Ratan is quick to tend to him, though, and Tagore indicates that "his longings did not stay unfulfilled." The postmaster is incapable of fending for himself when he is sick.
At the end of the story, the postmaster rejects Ratan's pleas to go back to Calcultta with him. The postmaster shows himself to be emotionally incapable of coping with Ratan in his life in the big city. Even though she has done just about everything that she could to integrate herself in his life, it seems that he does not want his routine in Calcutta to be disrupted. He shows himself unable to deal with change, and must lack some level of strength in dealing with the changes to his life.
When he leaves without Ratan, the postmaster wavers back and forth about whether he did the right thing. He caves into a philosophical approach that talks about "who belonged to whom in this world." This shows that he is incapable of effectively coping with the consequences of his action. He has to rationalize it with philosophical insight as a way to detach himself from the results of what he has done. If he has effective coping skills, he would be able to take ownership of his actions and their consequences.