2011 Z4 35i same issue. My dealer is fully aware of the issue. Under original warranty it is covered. According to my Service Advisor 2009-late 2010 builds problem can surface. Part has been updated
Wish I'd known before, I would have been a bit more forceful with Coopers.
At least the issue is on the forum for others to discuss.
Meanwhile I did take the cover buttons off the second hand one I bought from eBay, it was easy and I now don't have to look at the damaged ones anymore.