Please tell me you sent it registered or certified!
The problem is you waited for verification of receipt after the board met, why didn't you contact them around the 15th so you could have at least overnighted it.
The one thing you will learn in the military is don't assume anything when it comes to deadlines, always double check everything before the boards meet.
I would contact Maxwell today and see how you can rectify the situation. If you did send it registered or certified, than you have absolute proof to submit to them you did everything as directed. However, if you didn't than you need to be prepared on your next course of action in this matter.
Not to be rude, but pretend your on the other side of the phone, you said you mailed it, but have no proof, how do they know you are being honest and just didn't realize until yesterday that you missed the date, so now you will say it was the Post Offices fault.