I can't be sure but it sounds a bit like trouble I had early on. The data connection from my HP laptop to Mini CNC control box was through the parallel printer port. I decided to use my laptop USB port by adding a USB to parallel converter to the CNC control box.
"will stop for a split second and then continue across the cut" That is what you reported that closely resembled the issues I was having.
So the first question I have is whether or not you are using the USB port on your PC to communicate with your control. If so order a USB to parallel adapter. They are not expensive.