Persistent though odd cohort have sent back a negative response, I see (7)
I believe the answer is:
chronic
'persistent' is the definition.
(a chronic condition is a persistent one)
'odd cohort have sent back a negative response i see' is the wordplay.
'odd' indicates alternate letters.
'have' means one lot of letters go next to another.
'sent back' says the letters should be written backwards.
'a negative response' becomes 'no' (negative answer).
'see' becomes 'C' (the word for the letter, according to Chambers).
The alternating letters of 'cohort' are 'chr'.
'no' written backwards gives 'on'.
'chr'+'on'+'i'+'c'='CHRONIC'
'though' acts as a link.
(Other definitions for chronic that I've seen before include "(Of illness) deep-seated" , "Of illness, prolonged or constantly recurring" , "(Of illness) lengthy; very bad (colloq.)" , "Of a very poor quality" , "Deep-seated - long-lasting" .)