Originally posted by Complaintdesk:

Keeping visual contact with a critter being tamed is essential until one sees the taming acclimatization icons emanating from the creature being tamed. Losing visual contact with a wolf being tamed before this happens or the new day dawns can lead it to despawn.

I had once captured a 2 star wolf in a mountainside taming pit when I was attacked by a fenrig. I was attacked in the evening by a pack of 3 wolves, one of which was a 2 star. I ran toward my taming pit, killing the normal wolves along the way, having not succeeded but tried this before, I died in the process (from taking too much damage from too many wolves), the 2 star wolf was my focus. I was probably only 3-5 metres away from the wolf, which was still slightly agitated and had not yet eaten the food dropped in the pit. Not wanting to lose visual contact with the wolf I waited until the last second until the fenrig came to me and attack. When it was close enough, I took a step or 2 towards it and hit it twice with my porcupine killing it. When I looked back to my taming pit and the 2* wolf but the pit was empty and the wolf was gone, despawned. Moments after that the game music declared a new day had dawned, along with the day number onscreen. Having never had a creature despawn while taming, I must admit how ticked off I was at how quickly and easily the wolf despawned. I literally just lost visual for a few seconds while standing so close to it but the fact that this all happened on the cusp of a new day dawning made sense, in that I did not have visual contact with the wolf, and it had not yet begun to acclimatize at the dawn of a new day.

From what I understand about the night only spawned critters the keys to their not despawning is that they have begun to tame, like you said, by eating (with those cute little hearts floating up) and the player is within a certain distance. I don't think direct visual contact is required and frankly can keep them agitated and not eating. I've always dug a pit to trap the wolf and a little shelter right next to it with a campfire, etc. for the downtime. When I do approach I'll crouch and go to stealth mode to ensure the wolf doesn't know I'm there and get alarmed - thus slowing up the taming time.
I've not tamed any *wolves yet but have had several no-stars that I've trapped at night vanish before I read the fine print.