Why can't I Copy a Character Style?

Sometimes the menu item Format > Copy Character Style is greyed out, even though you know you have changed something in the formatting.

The most likely reason is that you changed formatting for the paragraph, but not for the character - at least not directly.

Here the paragraph is selected:
Note the character at the end of the word.

Here just a word is selected:
Change formatting for the paragraph, and the Character Style is not updated. Change formatting for a word or individual characters, and the Character Style is updated and can be copied.