I currently have a 350z myself and I do not know of any recalls for its tires. From your statement it seems that it could be an overuse of tires due to racing or burnouts. Depending on what year model you have the only issue that I could find that was tire related was that there was a Tire Feathering Issue on the 2003 350z. However, other then that there are no additional issues that I could find or remember hearing for that matter. If your car is under warranty or if you purchase the warranty, I would take it to the dealer and see what he can do to fix it. If not, I would take it to a reputable tire shop and mention the problem and they can get you a solution. Good luck with your problem and enjoy the 350z, I know I am.

         I had a 350Z from 2005 until just a few months ago. I traded mine in for an Infiniti FX. I loved my Z, just needed more space for the family. I never had any trouble at all with the tires or anything else for that matter. I did have to change to tires after about 2 years, but it was just due to wear and tear I had put on the car.