CHA advocates always leaving stirrup bar safety latches in the open position. It is highly unlikely that the stirrup leathers will come loose from jumping or any other activity when the latch is open and even if it does, the result is far less dangerous than the potential for being drug by a horse.
The releasable latch on the stirrup bar is called a ‘safety latch’ and is intended to be used in the up position and release in the event a rider falls and the rider’s foot is stuck in the stirrup. However, if the latch is not regularly cleaned and oiled, it freezes in the up position and does not function properly, therefore it becomes a hazard by locking the stirrup leathers into place. Since few riders will properly maintain the safety latch, it is best to leave the latch open.
Perhaps very high level cross country jumpers and open jumpers may choose to leave the latch closed, to prevent the possibility of the leather releasing unintentionally, but novice level riders and all children should err on the side of safety and leave the latch open. It is highly unlikely that the leather will release during the normal course of riding. Many English saddles made today do not even have the latch and instead have a curved stirrup bar that will cause the leather to release in the even of a dragging.