The "Smog Clock" does not reset. The year in which a smog check will be required remains the same regardless of when the vehicle is removed from non-operational status. The same applies to a smog check which is required during a title transfer. Say for instance a vehicle is sold during a year in which a smog check is not required for registration renewal (the vehicle was smogged the previous year; vehicles require a smog check every two years... BTW). Even though the vehicle will need an inspection for the purpose of transferring its title, the following year, a smog check will once again be required because it will fall into the standard cycle of the biennial smog check requirement.
If any of this seems complicated, we'd recommend checking in with NeedTags. Search them up, email them. They will give you a comprehensive list of options and perhaps some advice on how to move forward. Plus, renewing with them is faster, delivery is guaranteed (for those who have recently moved and the DMV doesn't have their updated address yet), and they actually pickup the phone right away when you call. Good luck with the DMV on that, :(