I was having a very similar issue and just wanted to make a quick post to let anybody else having this issue know what worked for me.
While making a fairly large sign (about 100 inches long), my MH-871 MK2 kept freezing in the same place. I narrowed it down to static because the cutter would cut just fine with no vinyl running through it, but hang up every time with vinyl in it. I was cutting on carpet using a USB connection and did not have a static wire-rope thing.
I was able to get one piece to cut by using a homemade grounding wire draped across the vinyl and by having a person on both the in-feed side and out-feed side holding the vinyl off the floor.
Things that didn't seem to help: homemade static wire. Placing ceramic tile over the carpet so the vinyl avoided contact with the carpet.
Final solution(s):
1. I installed the USCutter ground strap, rope thing. http://www.uscutter.com/Anti-Static-Kit-for-Vinyl-Cutters
2. I installed a serial card in my computer and ran a 25 foot serial cord to another room with a tile floor.
Since those upgrades, the cutter works great, every time.