This problem mainly arises due to the permission problems. If the logged in user do not have permission to make the changes to the appearance of the theme, then the changes he makes won’t be reflected.

Set the permission to 644 for files and 755 for folders will allow the privilege to make changes to the files using the customizer.

Click here to see a detailed explanation about the permission and their meanings.

For Directory and child themes

If you want to change the color of the elements of your Directory theme or any of the Directory child themes, you will be required to set the writable and executable permission  for the file /Directory/css/admin_style.css. This changes can be applied at the server end.