My house has the original opener that isn't rolling, it was built in 1983. Rolling code technology came out in 1993 [wikipedia.org], which really isn't that long ago considering how often you need to replace them.
Similar situation here. I have a side-by-side garage with two separate early-1980s openers manufactured by Overhead Door Company. Each opener came with two one-button remotes.
One of the openers was damaged in 1994 (a roofing contractor backed into the door with his truck), so we ended up with the old fixed-code opener on the left door and a new rolling-code opener (also by Overhead Door) on the right. The new opener came with a pair of three-button remotes. Two buttons are strictly for rolling-code openers, but the third button can do both fixed- and rolling-code. Now, I can open both doors with one remote. Very handy.
Anyway, the point is that some of these openers can last a long time. Like your opener, my remaining fixed-code example is verging on 33 or 34 years old. Considering how often it's opened and closed, it sometimes surprises me how it continues to operate so smoothly.