In JoJo: Diamond is Unbreakable, why didn't Joseph use Hermit Purple to find Kira's new identity? The whole point of bringing Joseph to Morioh was to make him use Hermit Purple.

So why didn't he use it to find Kira after he changed his appearance?
It's because Joseph Joestar is growing senile.
Stands are the manifestation of the user's spirit.
Remember that episode when Polnareff became young because of 
Alessi's Stand? Silver Chariot was weak when he was a kid.

Durability or Permanence is a category in a stand stat which also affects stands as they age too or when not in practice. (A great example would be Star Platinum's initial 1.5 second Timestop turned 2.0 seconds by the middle of Part 4. After the events of Part 6, Jotaro trained himself again to protect those he needs as he have learned in Part 4. He later regained his 5 second time stop, the maximum seconds the human body can achieve.)

So in a sense, if a stand user grows old, it affects also their stands. Likewise, if a stand is not used that much, it gets weaker. Hermit Purple is the stand manifestation of Hamon. As there are no more threats, vampires, and Aztec demigods, Joseph Joestar didn't use it that much (also Joseph Joestar isn't the kind of person to practice. He relies on his cunning). Should he still practice it, I bet he'd still look young even on his 50s in Part 3 just like Lisa Lisa.

On a hindsight, Hermit Purple's ability to search Stand Users was hazy because there are a lot of Stand Users in Morioh. Just like when he tried to divine Kira but found Angelo instead.

TL;DR Joseph Joestar can't use Hermit Purple efficiently because he is old and doesn't practice it that much.