The struggles I see Mr. Sweet and the narrator in "To Hell With Dying" going through are different.
Mr. Sweet seems to struggle with the unhappiness that has made up his life: not being able to pursue a career he wanted because of his race; having a son who was a user and never any help at all; and, losing his wife, whom he loved so well. With these things weighing so heavily on his heart, Mr. Sweet seems to struggle with staying alive. There are so many times he is at death's door, and it is the narrator and the rest of her family that love him enough to "revive" him so that he will stay.
The narrator's struggle would seem to be her dedication to keeping him alive. When she and her brother revive Mr. Sweet, it is not a chore for them. They love this man who most people would probably have no time for. However, besides the struggle to keep him alive, perhaps an inferred struggle comes at the end.
At the start of the story, when the narrator talks about visiting Mr. Sweet's house to revive him when his wife was still alive, the wife is moved away from the bedside, in tears. The narrator states, "...although she knew the death was not necessarily the last one unless Mr. Sweet really wanted it to be."
At the end, I wonder if the narrator struggles with this memory when Mr. Sweet dies because he had finally reached the point, especially with the narrator and her brother having moved away, where he wanted to die "for the last time." This might be part of the struggle the narrator is facing when at twenty-four, she cannot quite believe that she could not bring him back, revive him, once more.