The Alcoholics Anonymous textbook uses the word "recovered" about 15 times.
The preface says, "To show alcoholics precisely how we recovered."
The promise of the program of AA is not a perpetual state of battling alcohol. It is freedom. It's all there, in the AA text book. Check it out.
"Recovered" does not mean "cured." It means that one has had a spiritual experience sufficient to solve the alcohol problem. And Steps 10-12 show us how to continue to enlarge our spiritual life, so that problem remains solved.
"Recovering" is rehab speak that infiltrated AA, along with "One Day At A Time," "Just Don't Drink and go to meetings," and other slogans that can't be found in AA literature, because they run counter to what our program requires, and promises.