Question about Shadow reaper's trait

Hello, this is about Shadow Reaper’s trait. I’ve been using reapers with the Doombringer spec and I’ve had my Shadow Reaper kill my Gravebane wight, granting my reapers the ‘woe’ trait. However, when my own Reapers were to die the turn after they’ve gained the trait, the trait does not work nor proc, I was wondering if there’s any reason for this.