Okeke has trouble sleeping at the end of the story because he's in a state of emotional turmoil:

"That night he hardly slept, from remorse—and a vague fear that he might die without making it up to them."

He has just received the letter from his daughter-in-law, Nene, in which she begged Okeke to reestablish his relationship with his son, Nnaemeka (Nene's husband), and to meet Okeke's two grandsons for the first time.

Okeke has spent the past eight years in bitterness, refusing to see Nnaemeka, because of his marriage that Okeke doesn't approve of. Now, Okeke is a grandfather who has never met his grandchildren. Despite the cruel words and harsh silence Okeke has always extended to Nene, she has reached out to him with warmth, kindness, and respect, via the letter, and offered him one last chance to connect with Nnaemeka and the young boys.

So you can understand how Okeke feels "the resolution he had built up over so many years falling in," meaning that his harsh feelings toward his son are starting to crumble. He tries to "steel his heart" and avoid thinking about the grandchildren, and he tries to distract himself by humming a religious hymn, but he can't help visualizing the grandchildren and thinking about how he has essentially abandoned them since birth.

In sum, guilt, worry, and the sad realization that he must change are the feelings that are keeping Okeke up that night.