Does it work even when you move the character and/or rotate his torso, etc.? But the C stays behind?
Try grouping your clusters, then parenting them under the head joint. Make sure you've activated "relative" mode on the clusters or you'll get double transforms. Here's my cluster workflow for characters (as I've had weird problems before too).
1.) Use Edit>Paint Selection tool to select desired points
2.) Deform>Create Cluster-[] (envelope 1, relative off) - then click Create to make a Cluster out of points you had selected
3.) Select Cluster, then hit W key (Move tool) and then hit Insert key to recenter cluster pivot to the center of the eye so that it rotates around the eye.
4.) Use Paint Weights Tool to limit cluster influence as needed (may help to rotate the cluster to see how it responds)
5.) Reset cluster rotation to 0
6.) Click Cluster, then Shift-select the bone or locator under which it should be parented
7.) Hit 'P' key to parent cluster under the bone/locator - this will automatically create a group for the cluster
8.) In the cluster Attributes, check "Relative" to ensure that transforms are inherited only from its direct parent (e.g. the group node that parenting created).
9.) Check deformation order - select the mesh, right click &drag down to inputs->Complete list.
10.) Make sure eyelid cluster is below the skin cluster deformation. If it's not, middle mouse drag it below.
For additional documentation, see the lower half of
D:AWMaya3.0docsen_UShtmlUserGuideCharSetupDeformIntro2.html
(where D is replaced with whatever drive you have maya installed on)
I don't know if all these steps are really necessary - it's quite possible that they're not or that they can be done in different order. I just know that Steps 9-10 were the latest thing I tried & it now works. Prior to that there were wacky double transformations that would happen when the cluster was rotated & then the character was moved in multiple axes and/or rotated at several major joints.
Theoretically, creating the clusters before binding the skin alleviates the necessity of 9 & 10 as the clusters would then be evaluated before the skin tweaks, but I haven't tested this to confirm.
Here's more from the documentation:
A double transformation effect is where skin object points are subjected to the action of a joint more than once, resulting in extreme, undesirable shape changes. Double transformation effects can occur if the skin object points are also being affected by a deformer that is in turn affected by the joint's actions. For example, if after skinning you create a cluster deformer to further control certain skin object points and then parent the cluster deformer handle to the joint that also affects the skin object points, when you move the joint the points will be affected twice over by the joint's action.
Rule 1.) There are no rules