I find that many segments have heavy exposure for years, and afterwards it doesn't get aired for a long time, only for it to appear again some years later, and then get retired afterwards. This was typically the case with Muppet sketches. I remember several segments with Herbert Birdsfoot that didn't air for years and then reappear for its final airing. One example is his M and W discussion which was shown in December 1987 (Ep. 2383) and was never shown again until March 1994 )Ep. 3222) and after that it disappeared from the show. Another Herbert sketch that was absent for a long time was the one where Ernie tries to borrow Herbert's vacuum cleaner. Its second last airing was in March 1983 (Ep. 1796), and there would be a 12 year wait before its next - and final - airing in April 1995 (Ep. 3374). I also know the segment where he and Grover count to 20 - that aired in May 1977 (Ep. 1037), and didn't air again until February 1985 (Ep. 2036, its only airing in the 1980s), and disappeared afterwards. The segment in which Herbert explains the concept of shadows to Grover was shown in January 1981 (Ep. 1489), and there would be a wait of five years before its final airing in January 1986 (Ep. 2149).
It seems as if the show has a tendency to phase out segments by putting a lengthy gap between their final two airings, but this typically applies mostly to Muppet and cast sketches, maybe some celebrity sketches.
Regarding cast appearances in recycled segments after they left the show, I believe they aired the song and dance number about the letter K with Buffy and Mr. McIntosh as recently as March 1988, and it''s very surprising considering she left the show just before the end of Season 12 in May 1981, many years ago at the time.
I believe they aired "The Riddle" and "Singing in the Shower" - segments in which Olivia was involved - in the early 1990s, despite that Olivia left in 1988.
They also aired recycled footage with Mr. Hooper in an April 1985 episode (Ep. 2073) when the new human character, Piri, questioned Big Bird about Mr. Hooper and who he is (or should I say, was) and why the store is called Hooper's Store. This was meant to be a plot designed to be a remembrance of Mr. Hooper. Noggin aired that episode in their "Unpaved" package.