Sinking feeling, conclusively, during one’s breakdown (5,5)
I believe the answer is:
going under
'sinking' is the definition.
('go under' can be a synonym of 'sink')
'feeling conclusively during one's breakdown' is the wordplay.
'conclusively' says to take the final letters (the letter which concludes the word).
'breakdown' is an anagram indicator.
The last letter of 'feeling' is 'g'.
'during'+'one'='duringone'
'duringone' with letters rearranged gives 'oingunder'.
'g'+'oingunder'='GOING UNDER'
(Another definition for going under that I've seen is " Sinking, failing".)