The films have never been major box office draws, usually opening between $4 million and $8 million.
The Fate of the Furious held the number one spot for a second weekend, adding $38 million to its current $163 million domestic haul.
The Promise proved to be one of those stumbles, starting out this weekend with a ninth place wide release but only $4 million in sales against an estimated $100 million production budget.
The latest Disney nature documentary was the top newcomer of the week, but only managed a fourth place debut.