You can replace cables but what it sounds like to me is static. There is a way to remedy this problem by getting a schematic of machine and finding the main ground and loosen the screw and wrap a copper coated wire to the ground then down to the aluminum frame of your machine. I had an issue with my old machine 2 years ago and it worked like a charm. I thought about doing that to my new machine VE Q100 but so far no issues.
You will find that static at this time of the year will even effect the best of the best as well as the cheep ones. If it was stopping at the same time every time I would defiantly say to wire frame your art and look closely in the area it stops for missing parts (been there), but what you are explaining at this time of the year sounds defiantly like a static issue.
TRY THIS: Cut off 8" more then you need and SHEET feed it. Before you start the cutting wipe everything down, chances are it will cut properly then as the friction will be lowered greatly. If that doesn't work make notes and contact Graphtec. If you can pen it onto
paper then I would also think that it is a static issue as the
paper doesn't create static like vinyl.