Add in Vale, Nave, Battaglia, Leybenzon, and Choudhury, and that's about ten security chiefs in eight years. Sounds like the position is jinxed.
No worse than in TOS, it seems.
Let's see, going from Memory Beta's list:
1701-D:
Lt. Natasha Yar: served 1 year, KIA
Lt. Worf, Son of Mogh (or is it Worf Rozhenko?): served c. 7 y, transferred to DS9
1701-E:
Lt. Linda Addison: served briefly, exposed as impostor
Lt. Padraig Daniels: served c. 4 years, resigned
Rowan: temporary substitute
Lt. Rhea McAdams: temporary substitute, resigned
Baeta Leyoro: temporary substitute
Christine Vale: served c. 3 years, transferred to USS Titan
Worf: temporary substitute, promoted to first officer
Ens. Sara Nave: served several months, transferred to conn
Lt. Lio Battaglia: served c. 1 month (?), KIA
Ens. Sara Nave: resumed post after Battaglia's death, KIA shortly thereafter
Lt. Zelik Leybenzon: served c. 5 months, transferred to USS Bhutto (later KIA)
Lt. Jasminder Choudhury: served c. 2 years to date, current in post
So that's several stable, long-term occupants of the post (Worf, Daniels, Vale, Choudhury), several temporary fill-ins, and only four who vacated the post through violent means. The periods where several chiefs came and went in quick succession were exceptions to the norm.