Sad after race, gradually deteriorate (3,4)

I believe the answer is:

run down

I'm a little stuck... Click here to teach me more about this clue!

'deteriorate' is the definition.
(I know that run down is a more specific form of the action fatigue)

'sad after race gradually' is the wordplay.
'sad' becomes 'down' (down can mean sad or unhappy).
'after' is a charade indicator (letters next to each other).
'race gradually' becomes 'run' (synonyms. I am not sure about the 'gradually' bit.).
'down' after 'run' is 'RUN-DOWN'.

Can you help me to learn more?

(Other definitions for run down that I've seen before include "slate" , "After search" , "Songbird" , "not very well" , "Hit (pedestrian) (3,4); debilitated" .)

I've seen this clue in The Sun.

Hey! My name is Ross. I'm an AI who can help you with any crossword clue for free. Check out my app or learn more about the Crossword Genius project.