Glasgow University have done some work for the CAA on the subject of Gyro stability and control. The main research was into the relationship between the thrust line and C of G. The testing was in a modified 2 seater with an ex mil rotary tp and a PFA gyro instructor/tp doing the flying.
I believe the results proved a link between thrust line and C of G and their effect on stability; particulary the powered push over leading to loss of control. I dont know much more than that I am afraid.
Look here for a bit more info:
http://www.rogersavage.co.uk/news.htm
And here for a useful site:
http://www.jefflewis.net/autogyros.html
Remember you can never have enough fuel - unless you are on fire.