I agree just keep calling and emailing them. I wouldn't give you odds either way because it may be a case by case scenario.
The only thing I would say is that telling them you lost sight of the due date, is not a good image you want to portray to the people that are giving you money. In other words, it could appear as a non-chalant attitude re: the scholarship. You didn't mean that much to me to prioritize, OR I am poor when it comes to time management. Neither is a good way to start off a conversation. Before you call role play in your mind what you are going to say, and make sure when they come back with a negative response you have an answer ready for them. In other words be them in your mind in the conversation.
ESPECIALLY, since the AF is going through force shape re-structuring!
I would contact them over and over again, be a pain in their arse until they respond. If that fails, contact the det you expect to join, and see if they can give you insight.
Lesson learned, you are going to be seen in a few months as a possible leader in the military, and that will not float with the AF. In the real AF, and even AFROTC, due dates are hard and fast. When they say the paperwork is due by close of duty day on X date, that's it.