The Hind of Ceryneia was sacred to Artemis with golden horns and hooves of bronze and could not be hunted by ordinary men.
Possibly it was just some priestess' spoilt pet helping itself to local crops and gardens and just making a general nuisance of itself damaging gardens however it be have been sacred for other reasons too!
Legend and some historians speak of "Hyperboreans" visiting the shrines of Greece particularly Delphi following the Amber trade route.
Perhaps this deer was a reindeer hence its special status.
Now Ceryneia was the name of both a settlement and a river now called the Vouraikos, and this river that flows through a narrow gorge which is now notable for a scenic railway called the Kalavrita.
Due to the local geology the valley is broader up near Kalavrita and narrows to a gorge before reaching the narrows coastal plain.
Deer raiding gardens and farms near could have retreated into the safety of the narrow gorge and hidden in forested slopes difficult for even the most skilled hunters to access.
Heracles has said to have taken a year to catch the beast which may seem odd to modern hunters but remember he had to catch it alive to avoid offending the goddess or breaking a taboo. Also no infra red scope!
I can also see some one saying
"How can we avoid breaching the taboo on that pesky deer?
Oh hey that Guy over at Mycenae whats his name Heracles the one already working off a curse ..."
Some versions claim Eurysthenes was going to add the deer to his private collection but Heracles either arranged its escape or first returned it to his half sister depending on which author you read.
The vase painting I selected shows Heracles between Athena and Artemis.
He is shown breaking off a horn so perhaps there is a lost variant of the story in which he does that?