Passive mobs often run persistently towards the player when hit repeatedly

not a bug. those mobs doesn't care if the player is nearby or not
in fact, i see this more like a feature request than a bug

Indeed fleeing after taking damage is aimlessly, and always has been.

Nah, they run into the direction they got hit from

Can confirm

Using a command to attack the pig, and putting the player in spectator, makes the fact that this is not an issue more obvious:

The direction the pig runs is entirely random. If the pig used to run away from the player, then the change behavior would be valid. As pointed out previously by others though, it has always been random, so there is no bug.

Looks like you all are for some reason saying the bug does not exist, I added a demonstration

About the comment that said that they just run in a random direction, no they don't, sort of. They will first run in the direction of the melee damage (counter intuitive) THEN run in a random direction. You can test this out by spawning a bunch of stuff and hitting them in creative mode while flying slightly above them.

Adding on to this, for some reason if the animal is running and facing away from you, each hit you land on it will cause it to gradually turn towards you.

Thanks for the video. I think this is caused by the animal not choosing a new panic destination each time it is hit.

@j_p_smith finally someone gets it... the issue has been here since that update that made endermen faster, maybe older ones too actually

Update : Found out it happens to evokers running from players too