equipment recommendation – Camera strap does not stay on shoulder

I’ve been using a Blackrapid sport camera strap for a year now, and it works great, except while shooting. It is very comfortable while the camera is hanging and offers great support, but as soon as I lift my camera, the shoulder part falls down along the arm, since there is no weight keeping it in place. Recently I was wearing a jacket and didn’t notice it falling down, and the camera almost dropped to the ground.

Is this the way it is supposed to work or am I doing something wrong? I tried to close the under the arm part quite tight, and tried it loose, but nothing changed. Actually tight, it tended to pull it towards the arm even more. Is there something that can be done to prevent this?