It seems like a lot of recurring Muppet segments (though obviously not any of the short form series) have only one or two installments in their debut season and take a bit of time before they really get a big back catalog of individual segments.
For example, the first season had two Answer Lady segments, and a few more debuted in season two, not sure if any more debuted after that (or if there are any that the wiki doesn't have info on). And that's the only recurring Muppet segment in the first season.
I don't know if there were any seasons that had multiple Here is Your Life segments. The Oak Tree segment first appeared in season 4, loaf of bread first appeared in season 6, and there would be more appearing sporadically. Also seems to be the case with other recurring game shows Guy Smiley hosted. Actually,season 2 premiered the only two known What's My Part? segments, while the first two Beat the Time segments premiered in season 4 while later ones were spread out by many years (and I don't know what season/seasons premiered both Name That Sound segments).
I'll have to check, but I think Alphabet Chat would be the same way, only there were only five (at least known) segments between seasons 6 and 24.
The first Mysterious Theater segment premiered in season 20, then two premiered in season 21, then season 22 didn't have any (unless you count a street scene that involved Mysterious Theater), and then season 23 gave us our last segment.
Season 5 had at least two Super Grover segments premier,but then we got three or four additional segments in season 6, and then it looks like there were no new Super Grover segments until season 10, and after that, Super Grover segments premiered a lot more sporadically over the years (especially if you're just counting "The Adventures of Super Grover" and not other segments or episodes where he appears as Super Grover).
Monsterpiece Theater is a bit of a surprise. The first one, Upstairs, Downstairs, premiered in season 9, then the next one, Me, Claudias, premiered in season 12, two seasons later (though I think it was produced for season 11), then the next one, The Sound of Music, premiered in season 14. Currently I don't know if Chariots of Fur premiered in season 14 or 15, if it premiered in season 14 then that would be the first season to have two such sketches, but I don't think they really started to do a lot of different Monsterpiece Theater sketches until season 20,and then each of the next few seasons brought us a lot more new ones. I recently read that Jim Henson personally asked for permission from the real Alistair Cooke to spoof him for the segments,which seems odd to do if it were meant to just be a one-time spoof.
It looks like season 11 had only two Leslie Mostly Show segments (and so far, as more season 11 guides are being completed, I haven't found any guides yet that include second shows of either), while season 12 brought us four more segments (and each of the first three weeks of season 12 premiered a new one). It will be awesome if I see an episode page (probably a season 12 episode) to list one with a first appearance noted, or click on an image and see multiple episodes (of the domestic Sesame Street) listed under "what links here".
But there have been some recurring Muppet segments that had many installments in their premier season. Sesame Street News had five or six premier in season four (I wonder if any that premiered in season five were produced for season four),season three premiered at least three, maybe four, waiter Grover segments. Season 30 gave us many installments of Ernie's Show and Tell and Monsters in Day Care (not sure off-hand about Sesame Street Goes to Day Care). I think all three American Revolution segments debuted in season 19, and I think all three Miami Mice segments aired during seasons 17 and 18 (the Kermit one has a known taping date that reflects season 17 - and the 40th anniversary book shows a season 17 script page with one segment listed as "Kermit Meets the M..." before being cut-off by a page in front, I assume it's "Kermit Meets the Miami Mice" - while the recent spoofs compilation lists 1986 as the date for The Count segment). And many Roosevelt Franklin Elementary School segments premiered in season 4.
Of course, the many recurring animated/film segments had a lot of installments in their premier seasons (many only had segments that premiered/were produced for one season and then repeated for many years later), and the various short form segments, meant to air daily/every other day (and be their own individual show internationally), had many installments produced for their first seasons.
It's also weird how in the old days, when there were 130 episodes a season, recurring segments would just have one or two in their debut seasons and then new installments would be really spaced out in terms of debuts, while in the last few decades, with significantly less episodes per season, most recurring segments have a lot more new segments in their debut seasons (though, as noted above, these were meant to be shown almost every day and on their own internationally).
I wonder how the first in a titled recurring segment series was listed in scripts if its first installment was the only one in its premier season, especially something where the individual installments had titles announced (like, did scripts list the first Monsterpiece Theater as "Monsterpiece Theater" or "Monsterpiece Theater: Upstairs, Downstairs"? And that's assuming it wasn't just listed as "Upstairs, Downstairs", without the Monsterpiece Theater heading).
Then again, who knows how many individual segments from each recurring segment series ended up failing at testing and as a result never aired?