Once more losing heart to be inconsistent... (4)
I believe the answer is:
agin
'be inconsistent' is the definition.
I know nothing about this answer so I cannot judge whether it can be defined by this definition.
'once more losing heart' is the wordplay.
'once more' becomes 'again' (synonyms).
'losing heart' suggests removing the centre.
'again' with its centre taken out is 'AGIN'.
'to' is the link.
Can you help me to learn more?
(Other definitions for agin that I've seen before include "Dialect form of against" , "Against (facetious)" , "Opposed to local" , "Hostile to" , "Not in favour of" .)