Identify the evidence which supports the fact that, although Nick as a child, he loses some of his innocence.

Two elements seem to suggest that Nick has been forever changed by what he sees during his night assisting a difficult delivery and a related suicide. Hemingway's subtlety is apparent in this brief story, but careful reading reveals two things that are different as we finish the story.
First, if we look at the types and number of questions that Nick asks, we see a noticeable complexity in his latter ones. Instead of wondering where he is going, for instance, he is now seeking meaning behind what is happening. He sees a complexity to adult human experience that he had not noticed earlier, and the basic expository elements that Hemingway offers underscores that.
Next, we might look at the last sentence for an even more subtle change. In this sentence, we see Hemingway's control of language:

In the early morning on the lake sitting in the stern of the boat with his father rowing, he felt quite sure that he would never die.

Now, Nick (despite his seemingly preposterous claim of immortality) situates himself in relation to all sorts of things. The high number of prepositional phrases shows Nick in relation to other things, and those other things are like the things that cause adults to become aware of life's difficulties and the need to respond to them with courage and grit—rather than like the father, who was unable to bear his relation to his wife's suffering.