Very rarely.
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Very rarely — almost never.
When something happens once in a blue moon, it occurs so infrequently it feels almost exceptional.
The phrase refers to the rare occurrence of a second full moon in a single calendar month.
"Every Now and Then"
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Occasionally but with some regularity — not as rare as once in a blue moon
"From Time to Time"
—
Happening at irregular but not especially rare intervals
"Once in a Blue Moon"
—
Happening very rarely — so infrequently it almost seems exceptional