Progressive rock was very popular in the early 70s (Pink Floyd [prog or not prog???], Yes, ELP, etc. were all doing very well) and you could hear the prog influence in non-prog groups also with extended instrumental intros (I think of Boston's "Foreplay" as a tip of the hat to prog, or the entire structure of "Stairway to Heaven" or "Bohemian Rhapsody" for instance). So it enjoyed popularity and was an even greater influence on general pop music.
Prog did not remain popular in the 70s due to the rise of disco (I remember, I was there with elephant bells and platforms), yacht rock, punk and changes within prog itself. Girls could not dance to it, FM radio began shortening their format to run more commericals, leaving 12 minute long prog pieces for the "after midnight in my parent's basement" demographic. Remember, the guys in prog bands generally weren't lookers (which meant there was a lot of frustrated practicing going on during those difficult teenage years to make them approach prog to begin with), the songs weren't about girls, but about the solstice and, in its most shameless moments, wizards, swords and spells. Not exactly "Cause we're living in a world of fools / breaking us down/ when we all..." yeah you get the point. And as Waylon Jennings pointed out, rock n roll was really about one thing, and prog was sometimes too busy looking for that 12 sided die to be bothered with that - and besides girls liked Zep.
I think prog sensed its own bloat in the later 70s, and either folded or did a quick change. ELP never came back from Works Vol 1 (financially they couldn't), Yes convulsed and reworked itself into the enormously successful, colorful, Yes 2.0 with Trevor Rabin and bandanas for everyone.
Genesis was subsumed by the growing influence of Phil Collins who almost singlehandedly RULED the 80s AOR, a little-ahead-of-the-curve King Crimson became the "Discipline" era and not the Wetton era, and speaking of Wetton, Asia the "supergroup" spawned at this time, born when UK got ran over by an accounting firm, and soon all the really, really bad prog bands went back to the shire and found day jobs, or, sadly, did a pet-shop hairdo, an inch of foundation and took up pseudo-European synth rock. (Rush, well, let's just say I have theories about what happened to Rush after MP, but that's another pile of drivel about a hypothetical bus accident on Dec 31 1980 that could explain everything.)
By 1980, prog became pop-ish, tighter, and more processed - or it faded out, looking rather silly, and self-absorbed (not like us!). "Owner of a Lonely Heart," "Tom Sawyer," "Abacab," "Heat of the Moment," "Neal and Jack and Me" (not a hit), became the sound of prog. Some of it danceable, some of it sorta about girls, some of it under 4 minutes, and catchy. So prog was still there, but it wasn't your father's prog, it wasn't extended organ solos, a section of Hymalayan bells and rare prayer cymbals with accompanying Tibetan chants, or the usual multi-layered guitar solo anthems, jarring time changes or the fun of adding an extra eighth note the 3rd time through for the hell of it - but it was prog, sorta.
There were always bands putting out classical prog material but it wasn't until the rise of metal bands that prog joined with metal to make prog metal and bands like Dream Theater were born, and soon prog metal was (IMHO) the most visible form of prog for years.
Today there are a lot pf prog bands and some are successful (well, not your father's royalty payments, either, but successful). You have a lot of prog type artists and some fantastic new artists, some great artists from back in the day - and of course, some harmless, lovely cringe.
Prog? It's always been there, baby, it hasn't always looked good, but it's still here.
Back to "Siberian Khatru."