Painfully sensitive flesh lasting a short time (5)

I believe the answer is:

quick

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'short time' is the definition.
'quick' can be an answer for 'short' (thesaurus). I am not sure about the 'time' bit.

I can't explain the remainder of the clue.

Can you help me to learn more?

(Other definitions for quick that I've seen before include "Speedy" , "living" , "Fast; alive" , "Rapid" , "Prompt; intelligent" .)

I've seen this clue in The Telegraph.

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