There is a problem with a safety string, and it's associated brass clip, on either side of the soft-top. It's purpose is to pull back the fabric, and keep it out of harms way as the top folds down.
The flimsy clip can both 'let go' of the string, or just fall out itself, which in turn allows the scissor motion of the top mechanism to cut the roof fabric. You can easily check this with your roof in the half way position. It is very important you do so regularly, so as not to destroy the fabric of your top.
This is a known design flaw, BMW have issued a recall for it, so get it fixed while you are under warranty. The kit will remain available as a $120 fix after your waranty period is up.
The entire design of the soft top, even the frame under the canvas, changed during the run, and the Mk ll top was meant to have cured all the issues like the string breaks and the rear window fabric flap coming unglued.
I don't have the exact VIN of the change, but it was around 61300. If you order a replacement now it will be one of these as BMW took all the Mk l's out of circulation back then because of their problems.
Here is a useful link to the Z8 Club's fact file on the tops.