Mine's in hospital (3)
I believe the answer is:
pit
'mine's' is the definition.
(down the pit)
'in hospital' is the wordplay.
'in' indicates the answer is hidden within the clue.
'PIT' is hidden in the letters of 'hospital'.
(Other definitions for pit that I've seen before include "See 9" , "A hole as for coal" , "Hollow" , "Sizeable hole in the ground" , "Cavity" .)