Highly sensitive time for prayer, situation that’s awkward in retrospect (3-6)

I believe the answer is:

top-secret

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But I can't explain it at all! Could you help me understand?

(Other definitions for top-secret that I've seen before include "Of the highest security classification" , "Highly classified" , "Extremely restricted (information)" , "(Of information) strictly not for public consumption" , "Very hush-hush" .)

I've seen this clue in The Times.

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