A bad back but not dying (5)
I believe the answer is:
alive
'not dying' is the definition.
(alive is the opposite of dead)
'a bad back' is the wordplay.
'bad' becomes 'evil' (similar in meaning).
'back' says the letters should be written in reverse.
'evil' in reverse letter order is 'live'.
'a'+'live'='ALIVE'
'but' is the link.
(Other definitions for alive that I've seen before include "Breathing, existing" , "''Crying cockles and mussels, ..., ..., oh'' (Molly Malone)" , "Vital, vibrant" , "Alert, active" , "Go or walk briskly" .)