After the initial shuffle of a category, there is usually little reason to shuffle. If there are major changes to the category, maybe a lot of new songs added to it, then it probably could use a shuffle. Otherwise, the only reason to shuffle is to eliminate predictability. Like, "every time I hear that song, seems like a few minutes later this song comes up". I shuffle the Hot Currents weekly. I have 13 songs in the category and I schedule four an hour which gives me about 50 spins a week on each song in the group. Hot Currents schedules first, so the songs rarely have rule violations that might alter the scheduling order of the songs in the group. So, fifty times a week, the song at rank position #5 will be followed fifteen minutes later by the song at rank position #6.
As I write this the average time-spent-listening to US radio each week is just over fifteen hours and that total comes from a series of seven to twenty shorter listening sessions. The math indicates that the average listener would then hear each of my Hot Currents between three and four times in a given week. Would any of them notice "that song gets played a quarter hour after the other one"? Very unlikely. Still, if songs average eight to ten weeks in Hot Currents and the songs stayed in the same rank scheduling order their whole run in the category, then a few heavy listeners might come to notice some predictability. If they should notice it, I contend it would be with songs they don't personally like. Not every listener likes all the hits, of course.
So, I shuffle my Hot Currents once a week and just before I run the weekend schedules. I do it then because the next pass through the category after a shuffle will always result in some "Song Previous Day" violations. With the rank order change, many of them in the limited group will come up on Saturday close to the same time they scheduled on Friday. And what's the problem with the same song coming up at 6:20 two days in a row? Well consider listening habits. If person has to be at work at 6:30 every day, then they are in the car driving to work at 6:20 every weekday. I don't want to ever be playing the same song at the same time two days in a row. Since weekend listening patterns are so very different than weekday listening patterns, I figure if a Hot Current played at 6:10 on Friday and happened to get scheduled again at 6:10 or 6:20 on Saturday, it's reaching an almost entirely different group of listeners than the Friday group and so is not worth the trouble to edit it. And it's a bother to edit anyway because with a 3:15 category turnover, there's little wiggle room.
I also shuffle my Medium Currents each week as I'm scheduling three of those an hour and there could be some noticeable predictability as with the Hots. The large categories, I hardly ever shuffle. I schedule two Recurrents (recent hits) each hour. The slots are separated by a half hour. I'm playing four Power Golds an hour, but there are a few hundred songs in that group and the turnover is much longer. Nobody will ever detect any song-to-song predictability with those. Plus, by the time Music 1 gets to the larger Categories, the formatting rules kick in as half of the slots in the hours are filled by the time the Gold categories are scheduled. So Golds are less likely to always schedule in 1-2-3 Rank order; a bit of natural shuffling happens with these.
Now here is a big caveat. I often seen stations that have a large category that is hour-specific. That is, they have some hours in the week with ONLY that category formatted; like a nightly two-hour Oldies show. So, the songs in it are mostly going to all schedule in rank order. Depending on how frequently I ran such a program and what my listener statistics can tell me about my listener's tune-in patterns, I'd probably shuffle one like that every few weeks.