Crossword Genius

Show real stamina and support those people failing to complete programme? (4,3,6)

Ross

I believe the answer is:

stay the course

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

'show real stamina' is the definition.
I know nothing about this answer so I can't judge whether this works.

'support those people failing to complete programme?' is the wordplay.
I cannot really understand how this works, but
'support' could be 'stay' (stay is a kind of support) and 'stay' is found within the answer.
'programme?' could be 'course' (programme of study) and 'course' is found within the answer.
The remaining letters 'the' is a valid word which might be clued in a way I don't understand.
This may be the basis of the clue (or it may be nonsense).

'and' acts as a link.

Can you help me to learn more?

(Other definitions for stay the course that I've seen before include "Maybe last in battle" , "Stick it out to the end" , "Pursue a difficult task until the end" , "Keep going to the end" , "struggle to finish" .)

I've seen this clue in The Times.
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