I had the same issue on my 630, turns out it was the black cover itself. I pulled mine off and couldn't see anything wrong, put it back on and had the same issue.
I ended up enlarging that "clearance cut-away" on the right side by taking off 3mm off the edge closest to the front of the cutter. There are two machine screws that were just touching the cover. The cover caused just enough friction against the two screws to prevent it from freely moving back up off of the vinyl. Works perfect now....just thought I'd share!
-Codesource