One iPhoto face is unavailable for syncing to my iPhone in iTunes
The solution was simple enough. As written on faces missing in itunes when syncing with iphone: 


Close iTunes if it's open.
Take one photo of John Doe and name it something else (whatever, as long as it's a new, unused name), say Johnny.
Drag and drop all photos from John Doe to Johnny and answer Yes to merge them.
Rename the face Johnny back to John Doe and quit iPhoto (properly, with ⌘Q) to save the changes to disk.
Open iTunes and check to synchronize John Doe.