We've covered this a few times before so I'll try and run highlights by:
When a tyre shop repairs a tyre, they take responsibility for it being safe, rather than the manufacturer. In today's society many companies simply won't repair Z rated (high speed) tyres, ragardless of the chances of there being a problem being remote.
Phone around until you find a tyre shop that is prepared to repair Z rated tyres, as long as they remove the tyre, and fit a plug / vulcanised rubber patch from the inside, the tyre should regain it's original speed rating. I've done several track days with professionally repaired tyres
Jambo