This is not necessarily canon or whatever, but maybe the reason they had to stop using clones is that the facility on Kamino was destroyed, perhaps by rebels. That would explain it. It would be unlikely that there would be other facilities elsewhere that could do it on such a massive scale or as efficiently simply because the Kaminoans treated it like a business, and their cloning techniques were their trade secret. They would no more let that get out than the secret recipe for classic CocaCola or the eleven herbs and spices blend for KFC.
Also, the clones that were in use would have mostly died out by the time Luke Skywalker reached the age he was in the first three movies. They were created to age more rapidly so they could be trained and come online as adult soldiers within about 5 years, and I believe I read somewhere that they were only really expected to have a service life of about 20 years. You have to figure the Clone Wars were going on for some time before Palpatine became the Emporer, and then it took time for Luke to grow to his early adulthood, say 20-21 years old.
Another thing to consider I think is that once the Empire had been established, the need for a massive clone army was not as great. They Empire was not really at war, even with the rebellion, right away. Mostly, the task at hand would have been to police and patrol local systems that fell under the Empire's jurisdiction, and who best to do that than locally recruited humans?
Just my two cents.
And they can recruit humans to serve, face it like any government the military was likely a good job with options if your like Luke and not force talented being in the Imperial Navy was a way to see the universe and get paid with job training and mustering out benefits. Rome was a very similar set-up the legion once you mustered out assured a Roman land and money and for non-Romans adding in a chance at citizenship if not from Greece or Italy. No small consideration if one thinks about it and voluntary service is preferable to conscription or clones.