Entertainment Weekly's August 8, 2003 issue has a small article explaining why Harry Potter and the Prisoner of Azkaban director, Alfonso Cuaron, has already declared from his own lips as to why he would not continue on to the next movie:
"It was always only Harry Potter and the Prisoner of Azkaban for me. I never thought [seriously] about continuing." Though he was approached about doing HP4, prepping Goblet (slated for 2005) while finishing Azkaban (coming out next June) seemed to daunting.
"Frankly," says Cuaron, smiling impishly, "I'm extremely lazy." Still, he dreads bidding adios to Potter stars Daniel Radcliffe, Emma Watson, and Rupert Grint. "That will be very painful," he says. "They're growing fantastically as actors. But it's up to the next director to enjoy them."