It sounds like you are using the special case holders with the Zip Trim. Often when the holder is not tighten down enough, the cartage case will spin out of the holder as you pull the pulley to spin the case. The case "gauge" has a pin that will go through the primer hole in the case, make sure this pin is tight on the gauge and centered in the case before you pull the string on the Zip Trim.
(be sure you have re-sized the case and removed the primer)
As you mentioned you are doing 223/5.56 cases and often when they are extracted from an AR-15 the base of this rimless cartage gets messed up (bent) and will not fit flat into the holder, the only thing you can do about this is to tighten the case holder down as well as you can without over forcing it on the Zip Trim.
I went from the special case holders to the three jaw holder that is made for the Zip Trim and that eliminated many of the problems with the cases slipping out of the Zip Trim as they where being spun. It did not eliminate the case bases being bent, but the cases were held into the zip trim better.
http://www.midwayusa.com/product/352653/lee-zip-trim-case-trimmer-universal-3-jaw-chuck-case-holder
Short of using a different method to trim your cases, the zip trim will work, but take your time and pull the string slowly at the start of any trim to insure the case is in tight before giving it a strong pull.
Lee came out with a new cutter and trimmer that works much better than the zip trim and I would recommend using that. I use it for all my 223/5.56 cases. It fits into the press and chamfers the case as well as trimming it.
http://www.midwayusa.com/product/717013/lee-deluxe-quick-trim-case-trimmer
Good luck and stay safe.
Jim
