Why did Harime Nui's eye not heal?
Based on the Nui Harime wikia page, her eye was destroyed.


  Nui was distracted by the sound of Ryūko calling for her father, allowing Isshin to destroy her left eye with the purple Scissor Blade.


It's also worth noting that the Scissor Blades were able to 


  prevent Nui's arms from regenerating when they were cut off.


The power of the Scissor Blades are known to be the one thing that can cut through Life Fibers, and this is likely what prevents the regeneration of Nui's body parts that were removed by them, as it destroys them.

As an aside, in many anime and shows, when a limb or body part is destroyed, it is not able to be regenerated. The best example I can think of is


  In Claymore, when a claymore loses a limb, they can have it heal by reattaching the severed limb. However, when Clare's arm is destroyed, she has no arm until one is given to her by Irene.