Sorry to hear that news. Don't give up! It is a mystery sometimes.. I've been in for almost 9. Took 5 just to get in the door. I have been trying for over a year now to "try something different". It takes patience, tenacity, and networking..
You could call the manager of the TEB office, and ask him what you could do to improve. That is about it. Chances are, someone with Higher Veteran's preference (10-points for Purple Heart) got selected.
This is not always the case, but fairly common.
I'd also be on the lookout for Government 2181 Series positions. These are "aircraft operation". FAA "Flight Check" for example.
V/R