To add further detail, like Omm said, this all changed starting with the 2016 bid. That's when H.R. 636 went into effect. Contained in H.R. 636 is this language...
(II) <<NOTE: Deadline.>> are
eligible for a veterans recruitment
appointment pursuant to section 4214 of
title 38 and provide a Certificate of
Release or Discharge from Active Duty
within 120 days of the announcement
closing;
Since the complete hiring changes of 2014, the FAA has been getting sued...repeatedly. FOIA requests to further justify pending class action lawsuits have been prevalent. Long story short, the FAA is breaking the law if they hire you outside of 120 days, which makes them susceptible to further lawsuits. The FAA will check and recheck your application through each stage of the process. Like DankVectorz mentioned, even going as far as the rescinding of TOL's.
Ways around this...
OTS bid - the 120 days only applies to if you are claiming veterans preference. You can still apply via pool 2 if you are outside of 120 days
For the lucky ones - If you are outside of the 120 days and you continue to fall through the cracks in the hiring process, my best advice to you is to not tell anyone until you are sworn in and officially become an FAA employee. Up until that day, if FAA HR becomes aware of their error, they are legally obligated to rescind your TOL/FOL.