When units are hunting, they push an attacking order in front.
That attacking order keeps track of the target's last known position to efficiently hunt. However, if the unit goes out of LOS, ShouldAbandonChase triggers and the unit goes back to the gather order - which has a hopelessly out of date "LastPos".
This is highlighted in the replay below (the one same as D2071, run on rP22466), where a Nabatean Camel Archer hunted a deer (2406, the one going to the right). After a while, the deer goes in LOS and the units walks back home.
By updating the LastPos of the gather order as well, we can efficiently hunt and the entity does get hunted by the Camel Archer.