Description of a fortnight? It goes on for a while! (4,5,4)

I believe the answer is:

week after week

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'for a while' is the definition.
Both the definition and answer are adverbs. Maybe you can see an association between them that I don't see?

I cannot understand how the rest of the clue works.

Can you help me to learn more?

I've seen this clue in The Irish Times.

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