Just gonna copy and paste an earlier response I wrote...
They recently did a visual update for Udyr, Unfortunately it was just a slight model and texture upgrade, rather than being the overhaul he really needs. The chances Riot will update him again any time soon, let alone overhaul his graphics, is really low because of his four stance mechanic. It simply makes updates and skins a giant pain to make because you essentially need to do four times the work (five if you make a stanceless model for the start of the game rather than start in bear stance graphically).
They gave Udyr an ultimate skin so that they could hold off on making any more skins on him for as long as possible simply because it is so much work. He was one of the earliest champions to be added to the game, first after the official release if I remember right, and still only has three non-default skins, and Black Belt Udyr is just a recolor.
TL:DR He's just not popular enough to be worth doing four times the work for a single skin.