I use a very similar tool roll and I put a safety pin through the chord to stop it slowly coming undone while cycling. I'm not really in the market to buy a new one now, but you're in a great opportunity to make a roll that doesn't need a safety pin.
I think the choice of webbing can make a difference. Pictured on top is a soft feel webbing that although nicer did slip through. The one on the bottom is what I used as it was more secure.
I use a very similar tool roll and I put a safety pin through the chord to stop it slowly coming undone while cycling. I'm not really in the market to buy a new one now, but you're in a great opportunity to make a roll that doesn't need a safety pin.