I've done many playthroughs in version 3.4*. In some, it took me a while to get up to "superior" hide quality from "fine", and other playthroughs where I start getting "superior" hides almost right away and the quality never drops unless I make a big mistake (like leaving the skin to soak for too long). I almost always play a Northerner hunter, with her hideworking skill buffed up real high.
If you're experiencing this at such a high hideworking skill, I would actually look at your weapon stat, how high your proficiency is for the weapon you're using to kill the animal. Generally speaking, the more blows it took to kill an animal, the more difficult it is to maintain high quality of the hide at the end, even if the carcass itself looks fine and not "harmed" or "ragged". It's worse if the wounds are in the body or neck, but the same seems to apply (at least in my experience) whether the blows are limited to the head or not. And keep in mind that the lower your weapon skill, the less you're guaranteed to hit the animal where you want to, so you might have tried hitting it in the head but hit the shoulder or foreleg ("arm") instead.
It's kind of odd in a way, because point and edge attacks tend to do more damage to the hide, but they are also more lethal and allow you to kill the animal with fewer blows... I experimented with this on elks, using blunt attacks only vs a few sharp point attacks, and the latter option offers the better results by far. However, at that point my character was at something like 93% spear skill, so I can't guarantee the same will be true if your weapon skill is even a little lower (in the 80-something percent range, blunt attacks seemed to result in the same or better outcome).
Character attribute may also have something to do with it... for example, high strength might help make each blow more effective, and high endurance might improve how accurate your strikes are even when you're tired. (This is conjecture, I have not experimented myself.) As far as my experience goes, knife quality helps but is not crucial.