Here's my take on it.
Stormtroopers began as clones, in everything from AotC up until a few years after RotS.
As mentioned before, clones age twice as fast; this so so that the Republic could have soldiers at their prime age (20), while only needing to grow and train them for ten years.
Sometime between AotC and RotS, Kamino was attacked, and the prime clone (an exact genetic duplicate of Jango) was killed, leaving the Kaminoians with nothing to clone from (so it can be assumed that they stopped producing jango clones on kamino at that time, destroying the possibility of "younger" clones). The youngest generation was biologically about 10 years old (5 years real-time).
That's all canonical. Now, my theory;
After RotS, most clones would have reached an age of around 20-30 years in biological age. By the time of ANH, that would be 50-60, which is for all intents and purposes too old to fight effectively.
Before even ANH, the Empire controls practically every system out to the Mid Rim, and some beyond, of loyal citizens eager to support the new order. (Remember, the Empire had a lot of popular support among the lesser informed, and since the Empire controlled the holonet, the "lesser informed" was just about everyone.)
Cloning is expensive. Recruiting is not. Training and growing a cloned soldier takes 10 years. Recruiting and training civilians would take 1-2 years, if that. The Empire has only a handful of cloning facilities, but thousands of inhabited starsystems. And the Empire was infamous for going with quantity over quality (TIE fighters are a good example).
Why would the Empire spend all that time and money on growing another clone army, when they could recruit twice as many soldiers for half the cost and half the time?
Moo.