Probably the issue for you is that the tail wheel on the rear of the cutter is holding the rear up, and the front edges of the skids are being forced to carry all the weight on a few inches of width, and then being drug around as you make your turns.
Possible solutions include adjusting the position stop on the rear lift control (If your machine doesn't have one, it would be straightforward to make one out of a wingnut, bolt, and a few washers) for the easiest option. Another choice would be to adjust the position of the rear lift links where they attach to the lower arms: These frequently have multiple holes that allow the side links to be positioned higher or lower onto the lift arms. Finally, you may need to adjust/reposition the top link. Moving the link to the other hole(s) on the tractor end may help, as might lengthening the top link itself.
No matter what, the goal is to get the cutter to ride reasonably distributed between the tail wheel and the tractor, not skidding along as might a sled.