Demoralised person in divorce case losing right to support daughter (10)
I believe the answer is:
despondent
'demoralised' is the definition.
'person in divorce case losing right to support daughter' is the wordplay.
'person in divorce case' becomes 'respondent' (someone being divorced is a respondent).
'losing' is a deletion indicator.
'right' becomes 'r' (common abbreviation).
'to support' says to put letters next to each other (in a down clue, some letters hold others up).
'daughter' becomes 'd' (genealogical abbreviation).
'respondent' with 'r' removed is 'espondent'.
'espondent' put after 'd' is 'DESPONDENT'.
(Other definitions for despondent that I've seen before include "Heartsick" , "In low spirits" , "Lacking hope - ten odd pens (anag)" , "Discouraged" , "Down in the dumps" .)