Vexed nuisance made a mistake, losing heart (8)
I believe the answer is:
pestered
'vexed' is the definition.
(I know that vexed can be written as pestered)
'nuisance made a mistake losing heart' is the wordplay.
'nuisance' becomes 'pest' (I've seen this before).
'made a mistake' becomes 'erred' ('err' can be a synonym of 'make a mistake').
'losing heart' means to remove the middle letters.
'erred' with its centre taken out is 'ered'.
'pest'+'ered'='PESTERED'
(Other definitions for pestered that I've seen before include "Constantly bothered by deer pets" , "Harassed, annoyed" , "Annoyed with frequent questions or requests" , "Badgered with repeated requests" , "Annoyed continually" .)