The character's mouth does in fact open at other times, such as when panting (after stamina reaches 0) or when taking a breath with eagle eye.
Occasionally the mouth doesn't open at all for these instances.
I also noticed that the mouth doesn't open from weapon swings (which are accompanied by a loud yell). This is most noticeable during a sneak attack.
I propose the mouths be animated for all of these cases, so the player looks more natural in combat.
If you want to reproduce this bug/issue, find a mudcrab and let it attack you. Lower your weapons and rotate the camera to look at your face.
(Note: This was reproduced with an entirely new character/save file).