Although he tried his hardest to become a Gym Leader, his training methods became harsher and harsher as a result of his becoming more and more focused on his dream. The Nurse Joy from the Electabuzz and Scyther episode denied his petition to become an official leader.
He tried to recover from this development, but then found that his Rattata had contracted rabies. Releasing them back into the wild, he then had to release his Butterfree around the same time Ash did, and then discovered that his Beedrill had run away in the middle of the night. Sandshrew, his only remaining Pokémon, was slowly becoming disillusioned with its trainer. After being forced into a cage match with a Victreebel, Sandshrew had had enough, and attacked AJ with Scratch before heading back out into the wild to rediscover its heritage.
Following this, AJ fell into a spiral of alcohol and depression, and died in a gutter shortly after he was observed drunkenly ordering a fire hydrant to use Water Gun.
....or he could just be out on a journey like so many of the other trainers Ash and co. meet, but that's not as much fun, is it?