Do you have "profile" or type setting on your plotter? If so you should set one up for unlaminated vinyl and one for laminated vinyl. The cut depth and pressure is gonna be different for the two types and you might be getting a little resistance from the laminated vinyls which could - over the course of the cut - could pull the vinyl out of "alignment.
We have a roland and compensate by creating a bleed if possible, smaller area by doing more groups instead of one big one, and we do a enviro match before print and before cut. The y axis usually is ok, but he x is off 1/8" avery 4' or so. J