What brand hardware are you using? Reason I ask, is that I've always used an "eye-bolt" type connector with kevlar...with good results. If your inserting it into a dubro style threaded rod, therein probably is your prob. Any case, it's chafing the kevlar strands...yes it is strong...tensile strength wise, and won't stretch.....but it's susceptible to wear, more so then steel I think.
Look into Sullivan brand, or Don's hobby has the best stuff,,,the coated kevlar..that's da stuff I think. Don's has pull pull kits that rival all I think...good luck..I do hope this helps.