I tried to fly it again with two strings attached for extra strength. One string broke suddenly, and the other string pulled incredibly strongly. I quickly tried to wind in the remaining string, but about ten seconds later it snapped too. Admittedly, the wind was quite a bit stronger than usual, but I still needed stronger string if the camera was to be safe. When I was flying the camera rig, I noticed a lot of vibration of the rig.
Vibration is very unwelcome because it blurs the photographs.
A fast shutter speed can remedy this, but I am using a cheap compact camera with no control over shutter speed, so I have to tackle the problem at the source. The rig was attached to the kite line with a single string, so it tended to swing about like a pendulum in the air. I solved this problem by suspending the rig from two points on the line. This stabilises it a lot, but sudden movement of the line can still cause shaking. I then put two flexible kite spars onto the rig, pointing out at the front in a 'V' shape.