Fail to win compassion, become disillusioned (4,5)
I believe the answer is:
lose heart
'become disillusioned' is the definition.
(I've seen this before)
'fail to win compassion' is the wordplay.
'fail to win' becomes 'lose' (synonyms).
'compassion' becomes 'heart' (I've seen this before).
'lose'+'heart'='LOSE HEART'
(Other definitions for lose heart that I've seen before include "Start to despair" , "Become dispirited" , "Become disillusioned" , "Mislay a card" , "find discouragement" .)