Why didn't the Eight Tails' horns grow back? From Eight Tails article:

The lower left part of its horns was permanently sliced off in a battle with A, and the right horns were destroyed by its own point-blank Tailed Beast Ball when fighting the Ten-Tails.
Instead of hind-legs, its lower half consists of its eight tails, which resemble the cephalopod arms of an octopus. These tails will grow back in the event they are sliced off.

If the tails are able to grow back, then why can't the horns too? Since Gyūki is made of chakra, how was it possible to permanently slice off a part of its horns?
It comes down to the basic fundamentals.

The bottom half of the 8 Tailed Beast is an octopus, but the top is more bull like.

Bulls horns are like bone, unlike tentacles made of easily dividable cells, the horns of an animal do not "grow from the top but from the bottom upwards" they are like finger nails, the horns may eventually "grow" but not "heal".