Periods in which wandering ant makes no progress (9)
I believe the answer is:
Here is my best explanation:
'makes no progress' is the definition.
'periods in which wandering ant' is the wordplay.
'periods' becomes 'stages' (e.g. many stages of development**).
'in which' is an insertion indicator.
'wandering' indicates an anagram.
'ant' with letters rearranged gives 'nat'.
'stages' going around 'nat' is 'STAGNATES'.
(Other definitions for stagnates that I've seen before include "Festers", "doesn't develop" and "becomes inactive".)