It feels like too much of a coincidence. I could probably dig up countless logs of back to back procs.
Here's 1 example from last night's raid, 1 second gap 3 times in a row between 4 soul caps:
https://www.warcraftlogs.com/reports...38&view=events
Really feels like 1 second gaps between procs happens too often, perhaps the bad luck protection is reset if it tries to proc with the buff already up.