Here are some statements of Carpenters fans discussing about this question:
"They were literally toast by 1981 as far as hit radio was concerned. That they managed one last hit, "Touch Me When We're Dancing" was more a case of being at the right place and the right time with the right song. Their image among the populace and the radio industry was really poor. Their records began to test with "high negatives"; that is, through audience testing it was determined that if a listener heard a Carpenters track on the radio, they would more than likely switch the station. ' Tune-out' in radio is the worst-feared phenomenon, and the testing they do tries to ensure that no listener in the desired demographic is turned-off by any song in their rotation. It's enough that commercial breaks will drive people away, so they never want a song to send any listener packing. Commercials are a necessary evil as they pay the bills. Playing records is simply a matter of choice.
So, by 1981, it was pretty well determined that if you were aiming for the prime 25-44 adult demographic, you better not be playing any Carpenters tunes. "Touch Me When We're Dancing" somehow managed to cut through all of that, for a short time, and enjoyed a run on hit radio while it was on the charts, so given the climate, it becomes more and more remarkable that it did. But as soon as it started down the charts, away it went, rarely to be heard again on the radio.
Edited to add: It turns out that today, August 22nd, marks the 30th anniversary of "Touch Me When We're Dancing" reaching Number One on the Billboard Adult Contemporary Chart, where it remained for two weeks".
"The Carpenters decline here in the USA probably started during the Horizon album. "Mr. Postman" and "Only Yesterday" did quite well, the "Solitaire" was released and did not do well on the charts. The "A Kind Of Hush" album saw moderate success with the single, "There's A Kind Of Hush", but "I Need To Be In Love" did not do well, although still received decent airplay. No other singles from "Hush" made much of an impact. "Passage" saw "All You Get From Love Is A Love Song" get some airplay, but didn't make a huge dent in the charts, and "Calling Occupants" did not do well in the US. Then there was the single "I Believe You", released in 1978 which did nothing. It would later appear on "Made In America" in 1981. When 1981 finally came around, "Touch Me When We're Dancing" got a lot of airplay and was heralded as the Carpenters comeback. The single made it to #16 on the pop charts, #1 adult contemporary charts. THAT was nice, I remember, to hear the Carpenters back on the radio! No other singles from "Made In America" made any radio impact. The only future singles, post 1983 that I ever heard at all on the radio, and maybe only once or twice were "Make Believe It's Your First Time", "Your Baby Doesnt' Love You Anymore" and "If I Had You".
HOWEVER, in 1978, with the release of CHRISTMAS PORTRAIT, radio went crazy over Carpenters! Every Holiday season, starting in 1978 and continuing to this day (2011) The Carpenters are played in heavy rotation with songs from both Christmas albums. You never know which songs, radio will play them all. So that is a cool fact that was true in 1978 and still true today. It is pretty much the only time you can hear Carpenters on the radio, but hey, that's great!"
"I think the Carpenters had a few things going against them. First off, the thing that everybody loved about them, their MUSIC, was against the tide and more in the soft rock vein. This was their greatest strength and their strongest weakness, in my opinion. The same reasons they became popular would later turn around and knock them down. The album and single picture sleeves, early on maybe up until 1974 only hurt their image more. Then we have the CHOICE of singles pulled from the albums. Probably "Sing" cemented their image. A huge hit, but a career mistake. The Carpenters recorded so many GREAT songs on each album, yet were always trying for the trendy pop singles. "There's A Kind Of Hush", "Please Mr. Postman" were frilly throw away pop compared to some of the other songs Karen and Richard recorded at the time. And "Goofus"? Cute for an album cut, but not a single. So I believe these singles in particular are what turned radio all the way off. The singles from Passage and Made In America could have had a better chance if their image hadn't been cemented by then. No matter how great the songs were, their entire image needed an overhaul. Quite frankly, the only thing I think could have done that would have been Karen's solo project, with the more riskier songs included on her album".
"Another thing that may have hurt them was they lost their "edge" that they had in the early years. Look at the variety of sounds you heard on the A Song For You album. That record has country, rock, tender balladry and even comedy! Plus Richard doing some lead vocals. By the time they got past Horizon, it was all Karen all the time, and almost all syrupy balladry that was heavily orchestrated. If you heard Richard at all it was only in the background, and they got too serious. The sense of fun and adventure -- which was there on all of their first four albums -- was replaced by overly-fussy, obviously expensive productions. If you heard an uptempo song, it was a remade oldie. Cool asides like "Piano Picker" or "Flat Baroque" didn't happen any more.... but it was those kinds of "album cuts" that helped make the Carpenters albums interesting for repeat listenings and brought in more than just the ballad fans".
"Their back catalog sold cleanly over the years so A&M would've really had no reason to drop them if KC had lived since they were still generating steady income, even if the sales were stronger from an International standpoint post Horizon. I think several things started in mid 1975 that started the decline. May 1975 the Gold Selling "Only Yesterday" leaves the Billboard Top 10. Within 3 weeks their label mates and other female single male keyboardist duo The Captain & Tennille go to Number One with "Love Will Keep Us Together" and begin a period of fairly consistent success that runs parallel to the fallow pop chart period of the Carps. The C&T's material from a singles standpoint is consistently sharper and punchier. A lot of that has to do with Neil Sedaka penning half those Top 10's, a better choice of covers for singles ("Shop Around" has a much livlier arrangement than the bland synths of "There's A Kind Of Hush"), and the sensuality that Toni Tennille could express in their hits like "You Never Done It Like That" and "The Way I Want To Touch You" that K&R felt they shouldn't or couldn't do on record at the time. They also had a weekly Variety show from 1976-1977 and several TV specials after that to raise their media profile where the Carpenters did one hourly program a year. I'm sure Radio Station programmers when presented with the option of adding one act or the others new single went with the then more appealing to the masses C&T. Even over the AC charts where K&R had ruled the airwaves their chart positions began to fade to the C&T's. When A&M decided to move in the Punk/New Wave direction in 1978 with signing the Sex Pistols and The Police both acts felt the sting with the C&T "Dream" album and The Carpenters "Christmas Portrait" LP's getting virtually no promotion. Toni Tennille talks about having a conversation with Karen about this fact at the 1978 A&M Xmas party in one of Joel Whitburn's books, saying the label has forgotten what made them so large to start with. So the C&T leave, head to a disco label where they score one more smash, then disappear from the recording scene when their second Casablanca album gets no promotion due to the label disintegrating and their seventies image begins to bite them in the same way it does the Carpenters. This brings us to early 1981 when K&C, now past Richard's addiction and Karen's canned solo attempt came back after a 3 year hiatus to a pop radio market that was going through another "Soft" period so their type of material fit in radio playlists easier with the likes of Paul Davis, Juice Newton, Air Supply, and Kenny Rogers than it did with Donna Summer and Bee Gees disco records the prior few years . "Touch Me When We're Dancing" benefits from this environment and does better than any single since "A Kind Of Hush." Of course, their image was still seen as a major detractor to stations wanting to appear hip/current so it stalls at #16. Barry Manilow was also at this hurtle in the same period. Promo for the follow ups is lackluster due to KC's health and marriage disintegrating and another delay comes on the recording front so Karen can seek treatment in New York. Had Karen fully recovered and lived past 1983 I think the Carpenters days as a Top 40 Pop Act were done. Radio swung hard towards edgier sounds thanks to "Thriller" and the second British Invasion at that point pretty much ending all the seventies era pop acts chart success by 1985. It would've been the time for a "What's New" standards project and to just relax and work Vegas Casinos. Putting out a new album every couple of years since they would both want to be with their families. They wouldn't have gotten to number one but sold well nonetheless. Then the revival and new found appreciation that kicked off for the group in the nineties would've still occured and they could've enjoyed the fruits of that at any pace they chose".