Bog of despair (6)
I believe the answer is:
slough
I believe this is a double definition.
'bog' is the first definition.
(slough is a kind of bog)
'despair' is the second definition.
('slough' can mean a hopeless situation)
'of' is the link.
(Other definitions for slough that I've seen before include "A bog or marsh, perhaps of despond" , "Swamp; cast off (skin)" , "Berkshire town and local authority" , "shed covering" , "where friendly bombs were wanted" .)