CaptMJ always provides excellent advice, I'm certain from having time sitting as a panel member at one of these boards. As CaptMJ explained, this is likely to come down to a risk decision for the MIDN and in the best interest of the Navy.
I would highly recommend that your son think really hard about the root cause of the problem - need to be very honest and frank on why he has failed the last two PRTs (it sounds like it is only the run portion) - is it laziness, not running as much as he could, or something else (we don't need to know)? I am going to assume he passed his plebe year PRTs - why was he able to pass then, but not the last two? What changes were made after the first failed PRT? Are the changes working - is there a trend in the right direction? Is a little more time needed (specifically since you said he failed by just a few seconds on most recent) - if he ran the PRT today, would he pass? Outside of his last official PRT (the one that counts), has he done a mock PRT and what was the outcome (could help establish the trend in the right direction)? If one hasn't been done, can the company do one for him (not sure if this is allowed), informally, prior to the board?
Bottom line - when your son goes to the board, he needs to be clear on WHAT the exact problem (root cause) is and HOW he will fix it (the game plan) so this will be the last time this is an issue. This is the best chance he might have at getting a reprieve. Brutal honesty and being introspective will be far more appreciated (regardless of the decision) than trying to shirk responsibility. What does his chain of command think - from squad leader to Company Officer? Other performance and academics, I'm certain will be taken into consideration - but if he is doing average/well in those areas (i.e. they are not negative factors), the focus will solely be on the PRT. I'm not certain how much character statements, etc. will have on the board - because if there isn't really a clear path forward on passing the PRT - you can be the hardest trying individual, personable, inclusive, etc. (all the good traits of being a leader) but the fact is that USNA graduation might not be in the deck of cards. Not saying to forego character statements, but their weight might be insignificant to the actual issue.
At the end of the day, if your son is truthful on identifying what the issue is and how to go after it - there isn't much more than can be done or asked - what has happened can't be changed, you only can look at how you can impact the future moving forward!
As CaptMJ also mentioned, it may not be the answer you want to hear, but we are trying to be candid.