Rising dust storm continued (5)
I believe the answer is:
lived
'continued' is the definition.
(did not die so continued)
'rising dust storm' is the wordplay.
'rising' says the letters should be written in reverse (going up in a down clue).
'dust storm' becomes 'devil' (dust devil whirlwind).
'devil' reversed gives 'LIVED'.
(Other definitions for lived that I've seen before include "Escaped destruction" , "Existed or dwelt" .)