Trouble: every other part falling off rapidly (3)
I believe the answer is:
ail
'trouble' is the definition.
(synonyms)
'every other part falling off rapidly' is the wordplay.
'every other part falling off' means one should take alternating letters (every other letter is removed).
The alternating letters of 'rapidly' are 'AIL'.
(Other definitions for ail that I've seen before include "Worry" , "Afflict; suffer" , "upset" , "Trouble, afflict; be sickly" , "distress" .)