Why painting the face and perfuming the body should have persisted throughout recorded history has been the subject of a susbstantial amount of antropological and psychological speculation.
B. How painting the face and perfuming the body could be persistent.
C. That painting the face and perfuming the body are persisting
D. Painting the face and perfuming the body persisting
E. The persisting of face painting and body perfuming
A: " should have persisted" is awkward coz nothing is assumed here.
B: "could be" is incorrect coz the fact still continues to the present.
E: as Matt pointed out, it should have " persistance"
D is awkward coz what we need here is a clause be the subject of " has" .
C it is.