This first time I attempted to use a Lee collet neck die I had similar issues. I also have a Co-Ax BTW, but didn't think that had anything to do with the problem. I ended up taking the die apart and after inspecting it closely it occurred to me that the tooling marks and burrs left over from the manufacturing process were preventing the die from working like it was intended. So I took some wet/dry sandpaper (starting with 320 grit and going up to about 600), applied some oil to it and then polished the beveled end of the collet (the "fingers" for lack of a better term) and also the mouth of the collet sleeve (the small round piece with the hole in it for the mandrel) where it compresses the collet. After this I applied a dab of grease around the mouth of the sleeve and put everything back together. To say it worked 100% better after doing this would be an understatement. I've done the same thing to every other collet die I've bought since then and they've all worked fine, but you need to be aware of another potential problem.
After using that first collet die for a while I was going to take it apart, clean it and reapply some grease to it. However, I couldn't get the collet to slide out of the main die body. I discovered that the bottom of the collet had been dented by the opposing sharp edges of the press's floating shellholder jaws. The collet (and probably the whole die) seems to be made of fairly soft metal, plus its design just isn't compatible with the Co-Ax's floating shellholder jaws. So here's what I came up with: First I simply took a regular shellholder, placed it between the jaws where the case would normally go and did my sizing with the cases sitting in the traditional type shellholder. Of course the die had to be readjusted for the difference in height. This worked fine, no more dented dies, but sometimes the brass would stick in the die since there was nothing preventing the shellholder from slipping out of the press's jaws when extracting a case. To fix this I took a dremel tool and ground down opposing sides of the shellholder base, but I left a rim on each side (like the rim of a case) that would fit under the jaws so that during case extraction the shellholder would be held in place. Problem solved, no more dented dies and no more instances of the press failing to extract the cases. I've had nothing but perfect operation from my collet dies and Co-Ax press since.