Remained sober on air, with no backsliding (6,2)
I believe the answer is:
stayed on
'remained' is the definition.
('stay on' can be a synonym of 'remain')
'sober on air with no backsliding' is the wordplay.
'sober on air' becomes 'stayed' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'with' means one lot of letters go next to another.
'backsliding' says the letters should be written in reverse.
'no' written backwards gives 'on'.
'stayed'+'on'='STAYED ON'
Can you help me to learn more?
(Other definitions for stayed on that I've seen before include "Remained after others left" , "remained behind" .)