This is just an idea but I think the reason people can't remember her is because she's already dead and that the her in the movie is just times when her loved ones around her are remembering her. I think the movie is the process of the characters moving on from Azusa's death. Her dad seemed to be packing to move the first time he appeared which suggests that he's was trying to move on from her death as he probably didn't want to stay in a house that reminded him of his dead daughter. Later on in the movie was a scene when the moving truck come's but it seems like Azusa had no idea about the moving as well as the fact her dad didn't even notice her which showed he was starting to carry on with life again. Also the fact that after her dad moved she wouldn't have anywhere to stay suggests that she wasn't actually there when she met Takashi because over wise where would she have stayed, changed clothes, etc. Also throughout the movie she's shown in very similar clothes in each scene which could have been Takashi's faint remembrance of her style. If she had worn the exact clothes in each scene it would've been too obvious about the actual story plot. I don't know, it's kinda hard to explain.
In the movie they also say that Takashi became more of a recluse which suggests that he got depressed after she may have died. He seemed to have begun to deal with her passing and in so started forgetting the times they spent together and even what she looked like, yet later feels guilty for forgetting and so tries to remember the times they spent by revisiting the places they went together.
I think the end of the movie where she's disappeared and he's running around searching for her, screaming 'sorry, Azusa', shows his denial about her death. Still having the feeling that she's there, even though he knows she's gone.
Sorry for the crappy explanation but this is the only thing I could think of that would explain why no one could remember her. I tried looking for what happened in the original novel but without luck. Anyway, I could be wrong but whatever.
In the movie they also say that Takashi became more of a recluse which suggests that he got depressed after she may have died. He seemed to have begun to deal with her passing and in so started forgetting the times they spent together and even what she looked like, yet later feels guilty for forgetting and so tries to remember the times they spent by revisiting the places they went together.
I think the end of the movie where she's disappeared and he's running around searching for her, screaming 'sorry, Azusa', shows his denial about her death. Still having the feeling that she's there, even though he knows she's gone.
Sorry for the crappy explanation but this is the only thing I could think of that would explain why no one could remember her. I tried looking for what happened in the original novel but without luck. Anyway, I could be wrong but whatever.