Slowly but surely go down? Pervert! (10)
I believe the answer is:
degenerate
This clue is a double definition.
'slowly but surely go down?' is the first definition.
'pervert' is the second definition.
('degenerate' can be a synonym of 'pervert')
(Other definitions for degenerate that I've seen before include "Immoral" , "base" , "dishonourable" , "Get worse" , "Corrupt type" .)