Respecting your character’s background
Your characters will evolve throughout the story or a series. They will naturally evolve and will become deep and complicated; their personalities will start showing more strength and charisma. If you are attuned to your characters you will respect their evolution in your writing. A character that was bubbly in the beginning of the story, but has gone through a lot of heartache and difficult situations as the story progresses should not be presented in the same way – the situations that you create for your characters will permeate their personalities and modus operandi. Ignoring that important part, will result in a lack of credibility and will make your writing appear fake. Readers interact and identify with your characters, they feel what the characters feel. If a reader does not “feel” a character, he/she may get discourage and stop reading or lose interest in the story.
By being true to your characters, you are engaging the readers and respecting them.
Inkspeare 
Some good advice. Characters who evolve feel more real and are easier to connect to. Also, they are more interesting than the character that remains still. That isn’t to say they need to have a complete personality transplant but that the reader needs to see the subtle changes that people go through.
Thanks for sharing this post.
Even in Children’s books – where some characters may remain the same, there is a small sense of evolution, according to the story, slight, but it is there. A very good example is The Miraculous Journey of Edward Tulane by Kate DiCamillo – one of my favorites.