Taken from the official Bridgestone site
http://www.runflat-system.com/english/qa/index.html
------------------------------------------------------------------------------------------------------------------------------
Is it possible to repair a Run-Flat tire that has been punctured?
It depends on how far and at what speed the car was driven after the puncture was sustained. Repair is possible only if deemed so by the tire sales store.
Preconditions include a puncture of less than 6mm for both side-reinforced type and support-ring type Run-Flat tires, plus minimal damage to the support ring in case of the latter.
However, it is strongly recommended that the tire is replaced as its durability will have been weakened after being repaired.
-----------------------------------------------------------------------------------------------------------------------------
I got a puncture 4 months ago on holiday in Corfu (Greek Island). BMW told me that
- they never repair the bridgestone tyres
- I was 250km from the nearest official BMW dealer, so therefore I needed a tow
- my tyre was incredibly rare and would take 5 days at the very least to ship from Germany
After this truly enlightening conversation I realised that actually I needed Bridgestone, not BMW. With a wonderfully helpful hotel owner in charge I got a new one couriered to the island for next day fitting, brilliant!
Just for reference, mine was not repairable; I had to drive around 50km on it to get back to my hotel base. I could tell from the noise and handling in the last 15 km or so, that this one was not going to work.