Whirlybird,
I believe that Mel Morris-Jones has a health concern, and it is very serious.
Gyrocopters do have a high rate of accidents, particularly in the United States.
As Flare Darnit
says, the primary problem is not a mechanical one. It is one of overall design and pilot education. The most popular designs have pusher props and very close-coupled tail-feathers. Some of them don't even have the horizontal tail. This results in stability problems, and since it is a 'low cost' sport, little money is spent on training.
It is still unknown if the FAA will allow gyrocopters into the new US Sport Pilot / Light Sport Aircraft category.