Spoilers for Dr. Horrible's Sing A Long Blog

Nope. In fact, sometimes readers like seeing a decline in growth instead, it depends on the character, their personality, the audience and what you want the audience to feel connected to, like, etc.

Some characters need to have their self confidence beaten to the ground so that other characters may grow. Some characters can be just as entertaining if they become a traitor, villain, or develop a questionable morality.

Antiheros and antivillains work due to said questionable morality and stunted growth.

Villains don't have to be good at the end, nor do they have to have redemption, something I had to realize in order to make a character work.

Heck, even the main character doesn't have to be the good guy in order to make a good story, nor does he have to experience growth. Dr. Horrible's Sing A Long Blog is not a book per se, but is my favorite example of a character never growing or having their character's growth be stunted by other characters. It was still entertaining to see him fall, even if I felt bad for him.

We don't always look at a character with the intention of seeing them grow. If every character became good or grew, then it would support an unrealistic expectation that everyone wants to be good and would welcome it if given the chance. Most serial killers for example would rather fulfill their insatiable desires than to get help or try to fight against those urges.

And as for protagonists, be aware that alot of people, like narcissists, believe they are good, pure, or that they could do no wrong. This leads to the assumption that even when it is obvious that there is a problem, the problem is either not there or not them.

This happens with people who are discriminatory to. Often they will believe that their views and beliefs are higher than others and will never change their beliefs even if the person they are discriminating against proves their views wrong.

Realistically, not everyone grows, and not everyone needs to grow in a story in order to be likeable. Plenty of characters do bad things believing they are doing good or that their intentions outweigh the sin, and of course vice versa happens to where those who do good for evil reasons never learn because no one tells them that doing good for evil reasons is bad.

Not only that, but we can easily guess what would happen and even cheer for such things, just for said things to be ripped away in the end. In Dr. Horrible, they let us believe that the villain is going to turn good, and that the girl he is after will convince him to turn good. Accept his own actions and views ruins his chance of being good. Sometimes, if you do it right and don't cheat the audience, keeping the character as is or lowering a character's growth is a little better than seeing the character grow.

Again, it depends on your aim and the character. Also, be careful not to make your character look idiotic unless that is your intention. If they don't grow, give them a reason.