Run Flat tires are more difficult to repair than regular tires. There was a very good article recently in the Globe & Mail's Drive section- see extract below
Lou's Garage - run-flat tires and why they’re not as easy to repair once punctured.
First time owners of run-flat equipped cars are almost always caught off guard when they arrive at their dealership to have one of those tires repaired due to a nail or puncture. What they expect is the prompt repair or patch, but what they get is an estimate for a replacement tire. If they are lucky, they will only need to purchase a single tire, but more often or not, if their vehicle is of the all-wheel drive variety, they will be pushed to replace the tires in pairs. So much for a simple tire fix. Adding further insult to injury, the cost for run-flats in some cases is as much as 30 per cent more than a conventional tire.
Run-flats, or zero pressure tires, have one distinct advantage. If you ever do get a flat, they can be driven on with zero tire pressure or for approximately 50-100 kilometres, which should be more than enough time for you to get to an auto repair shop. Vehicles from BMW, Mercedes-Benz, Mini and many Cadillacs come standard with run-flat tires, which accounts for about 14 per cent of the tire market. These auto manufacturers save on weight, which boosts fuel economy due to the lack of spare tire, jack and tool kits. This fuel economy boost may be minimal, but the engineers at these car companies know that most of their customers don’t change their own tires and instead opt for roadside assistance, so why not take the weight savings?
In addition to the added cost as mentioned above, reduced tread wear is a common complaint for run-flat tires; in other words, they wear out faster. The sidewall does all the work in any zero-pressure situation and must therefore be reinforced and made of heat-resistant rubber, making them far less pliable than a conventional tire. This thicker sidewall produces a noticeably harsher ride, forcing the tire manufacturer to seek a solution to soften the driving experience. Using a softer tread compound achieves that and offsets the roughness, but unfortunately does so at the price of tread life.
So, can you repair a run-flat? The answer is a firm maybe. If the sidewall indicates “do not repair,” then obviously the answer is no. Alternatively, the tire manufacturer Bridgestone’s FAQ section writes “some punctures may be repaired under certain restrictions.” Finding a tire professional and having them inspect the tire to see if it meets the criteria necessary for repair is mandatory. However, I highly doubt that your dealer service department is going to offer you that service, as most auto manufacturer literature prohibits run-flat repair. You are free to go outside the car dealer environment and visit a recognized tire dealer for the brand in question and ask them for a second opinion.