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 subsidiary indication.
'periods' becomes 'stages' (e.g. many stages of development**).
'in which' indicates putting letters inside.
'wandering' indicates an anagram.
'ant' anagrammed gives 'nat'.
'stages' enclosing 'nat' is 'stagnates'.
(Another definition for stagnates that I've seen is "Festers".)