Crossword Genius

A note to the girl who's falling down on the job (6)

Ross

I believe the answer is:

remiss

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'who's falling down on the job' is the definition.
I can't tell whether this defines the answer.

'a note to the girl' is the wordplay.
'a note' becomes 're' (as in do-re-mi).
'to the girl' becomes 'miss' (term of address for an unmarried woman).
're'+'miss'='REMISS'

Can you help me to learn more?

(Other definitions for remiss that I've seen before include "Negligent in performance of duty" , "Negligent, slack" , "Failing in what duty requires" , "Failing in one's duty" , "Derelict in duty" .)

I've seen this clue in the Evening Standard.
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