Just gave it to her recently, as she just got back from vacation, but with an unburnished leather cord like I made, it has enough friction to not open up on its own during every day use.
In fact, it can sometimes be annoying to open it up due to how much friction the unburnished leather fiber has.
It'll become easier to open with use, as the cord smoothes out, but if that's an issue, burnishing the leather or using a rounded leather cord may be a solution.