According to Manish Mehta:
Jets director of football administration Ari Nissim won't have contract renewed, I'm told. He was Tannenbaum's right-hand man on contracts— Manish Mehta(@MMehtaNYDN) May 15, 2013
Conor Orr had this to add:
Hearing Idzik negotiated majority of deals upon arrival + has a different contract preference/style which may have prompted Nissim move #nyj— Conor Orr (@ConorTOrr) May 15, 2013
Which isn't a surprise, really, as the contracts negotiated in the past few years contributed significantly to why the Jets are in this position anyway.
Finally, Albert Breer had this to add:
Feeling at the top of the Jets organization that people in personnel dept. had become too comfortable. A post-draft shake-up was inevitable.— Albert Breer (@AlbertBreer) May 15, 2013
Conor Orr has also noted that many of the front office personnel were hoping Cohen would get the job as General Manager to avoid exactly this type of house cleaning. Well, let's just say they gambled on the wrong horse. Maybe if (many of them) had done their jobs better, this wouldn't be necessary.