I think the new factory built machines are far less prone to inflight failures however autogyros do not respond well to pilot error during takeoff and landing. Essentially there are three main issues as far as I can see:
Firstly, a forward airspeed that is too high for the current rotor RPM as a result of pilot error during takeoff or landing, will result in an uncontrollable rollover because the blades are unable to flap to equality (unless the pilot is quick to push the stick forward to reduce the angle of attack, whilst simultaneously reducing airspeed).
Secondly, landing in a crosswind, pilot error can result in drifting or crabbing during touchdown, and with the tricycle undercarriage and relatively high CofG, coupled with the lift vector from the rotors, you can find yourself experiencing dynamic rollover very quickly.
Thirdly, during takeoff or go-around, finding yourself behind the drag curve and running out of clearway! This is a particular problem in a crosswind partly due to trying to avoid the second point of drifting or crabbing during ground contact. An autogyro requires an acceleration in ground effect phase, in order to get on the right side of the drag curve. But if you continue sideslipping once airborne in a strong crosswind, you're giving yourself an awful lot more drag which in many cases can result in very little acceleration. The pilot needs to recognise this lack of acceleration and commence crabbing whilst being very careful not to make ground contact again. At the same time, they need to remain very alert to the requirement to immediately re-enter sideslip should ground contact be required again.
All three of those gotchas are actually very closely linked and are occurring whilst very close to the ground. It's easy to see why people come a cropper with them, and in all honesty, I'm not entirely sure they are super well understood by low timers.
The high accident rate is due to the fact that generally, people buy an autogyro and then are trained on it, or they train an a school gyro and then immediately buy one. A lack of practical experience and an inadequate understanding of the issues, results in the accident rate that we see. Personally, I think the training of the fundamental understanding of these threats and what to do should you suddenly realise you're in imminent danger of experiencing them, could be a lot better.