I also have my LAST Sears garage door opener. Two remote controls have quit and had to be replaced but we thought that the feature in our car to remotely open the door would take care of the problem. WRONG! The rolling codes will work with only one car and when we tried to program the second car, it wouldn't work for the first.
Maybe all the new openers have this feature, but we will look for one that meets our needs and it won't be a Sears.