Even cigar going out may be source of complaint (9)
I believe the answer is:
grievance
'be source of complaint' is the definition.
(someone might complain about a grievance)
'even cigar going out' is the wordplay.
'going out' indicates an anagram (out can mean wrong or inaccurate).
'even'+'cigar'='evencigar'
'evencigar' with letters rearranged gives 'GRIEVANCE'.
'may' is the link.
(Other definitions for grievance that I've seen before include "gripe" , "Reason for dissatisfaction" , "Item causing resentment" , "Bad feeling" , "beef" .)