As an expression of time, its origin is a relation to business hours. 24 hours is "we don't close overnight." 7 days is "we don't close on weekends." 365 days is "we don't close on holidays." Those are the standard periods of unavailability.

If the sole holiday were a single Golden Week sometime in the year, the idiom may indeed have been "24/7/52", but holidays are simply scattershot like that.