I think most Nanos do not have the "overvoltage on reset" fix Google Code Archive - Long-term storage for Google Code Project Hosting., which COULD (maybe) lead to corrupting the bootloader. "Throughout history" there have been reports of the bootloader somehow being corrupted by a user sketch. I don't think we've ever tracked down exactly what happens (this SHOULD NOT be possible. But it's happened to me, too.)
Certainly re-programming the bootloader is on a "broken" arduino is worth a try.