How again was it

The first step to understanding the role of again here is to realise that it does not modify any particular part of this sentence, but rather the sentence as a whole. Its syntactic role would probably be clearer if it were separated by commas from the rest of the sentence.

What the word conveys is that one is aware that the matter has been discussed before. Why would one raise the matter again, if one is aware of its having been discussed before? It could be, as LPH has explained, that one has forgotten what was said then, and is asking that one's memory be refreshed. If the sentence is taken at face value, that would be the explanation.

The questions of this kind are, however, often used as rhetorical devices, and not intended to be taken literally. Chances are that the boy in the OP's example is not literally asking to be reminded of what was said in some previous conversation. After all, if they are both about to jump, there is no time for that. The boy hasn't literally forgotten the reasons that led him to agree to try sky diving. It is rather that now, that the jump is imminent, the reasons don't seem as convincing as they did before. The sentence was probably intended as a figure of speech, expressing his present fear and hesitation.

One could easily imagine other scenarios in which the questions with again would be used in the same way: 'Why, again, are we going on this hike?' (asked as one is waking up, and staying in bed seems much more appealing), 'Why, again, am I supposed to go on a diet?' (asked as one is eyeing a large slice of chocolate cake).