If this only happens when you turn the head and it is a simple sprite-based 360 head, in composer mode, click on your head and select face, then "Sprite Editor". You'll see a popup like this:
75% of original size (was 671x19) - Click to enlarge

When you click on the center head icon, you should see your face sprite in the box. Now click on the left-facing head icon and right-facing head icon (and also the intermediary circles). If there is no image in those boxes, then that might be your problem. Load the same face you had in the front-facing view in each of these (just the face!!!) - you'll be deforming it to suit later when adjusting the angles on your simple 360 head. Now go back to 360 Head Creator and check to see if that worked by checking the side angles; the face AND features should be there. Then you can go ahead and fine tune and tweak each angle of the head and features with deform/transform, etc. in 360 Head Creator [that's the painstaking part]. All your other sprites should not have to be replaced - for some reason, if the face isn't there, they don't show up in the angles.