As I tell people: If you remember when rock music was considered a fad that would die in two years, you are old.
Well, rock is now considered a classic form of music. I am so glad I got to see its beginnings, and to witness that historical event.
But when did it happen? HOW did it happen?
No way I would address this. It’s way too complicated and involved. 
I just wanted to say something I remember hearing years ago about Frank Sinatra, and that is, before he came along, in general kids listened to the same music as their parents. It was only with the rise of the young Sinatra that record companies realized the extent that kids had money, and would be willing to spend it on their “own” music. People often make an argument about what the first rock and roll song was. I would argue that Sinatra might have been the first “rock star”.
I would say that Frank was the first “Pop music” star, for varying definitions of Pop music, but he definitely wasn’t a rock star (except for the lifestyle, but “artist gone self-indulgent asshole” didn’t start with Frank. 
)
Rock moved into the ‘classic’ territory once the first ‘rock’ song passed the age of 50. The precise time that happened is up for debate.
Is there a name for rock music between the classic rock period and hair bands? I’m thinking more like 1980-1985. Classic is rock music before whatever happened at that time.
As far as I know, there aren’t any generally accepted terms deliniating those two periods, and radio stations vary in what they define as currently belonging in the “classic rock” format (both in terms of artists, and time frame).
FWIW, the SiriusXM satellite radio service has two Classic Rock stations, one focusing on the earlier period (from around 1965 until somewhere in the mid-to-late 1970s), the other focusing on the later period (from around the mid 1970s to the late 1980s). The first format is heavy on performers like Jimi Hendrix, The Who, The Doors, late Beatles, The Rolling Stones, early Bowie, etc. The second format is heavy on performers like Van Halen, AC/DC, Boston, Foreigner, Heart, Queen, etc. (Of course, there are some bands, and even some songs, that are on the cusp, and get play on both stations.)
The names of those stations reflect the musical medium of those eras: the former is called Classic Vinyl, the latter Classic Rewind. In their on-air promotional messaging, they sometimes refer to Classic Vinyl as songs from “the first generation of classic rock,” and on Classic Rewind as “the second generation of classic rock.”
I’ve heard it called arena rock. Queen, Van Halen, Journey, Boston, etc.
Don’t you remember? 
If you remember, you weren’t there, man.
More or less it began when nostalgia for the 50’s era kicked in. I’d say roughly mid 1970s:
Crocodile Rock, 1973 Elton John
Happy Days 1974-1984 ABC television
Whatever Happened to Saturday Night 1975 Meat Loaf
*Sha Na Na *1977; earlier band performances.
The Buddy Holly Story 1978
Grease 1978
A whole bunch of things happened close together in the 1960s.
The Beatles seemed fresh and new and critically important in the dark days after Kennedy’s assassination. They also made it really hard to say that rock music was idiot junk that was fit only for illiterates. The British Invasion groups piled on that and Dylan going electric brought the intellectual folk movement crowd over, after some disdain. When Leonard Bernstein started doing tv specials extolling rock music, it became too respectable - and cool - to ignore.
Rock also went from singles to albums. Singles were for teens; albums were for adults. Older rock albums could be dismissed as a hit single or two and filler junk, but Sgt. Pepper, Dylan, and the other albums designed to be albums killed that. The Billboard Album list was dominated by movie soundtracks in the first part of the 1960s but rock took that over too. Stereo albums first appeared in large quantities only at the end of the 1950s. All the early 60s rock came out in mono. By the mid-60s, though, rock albums were designed for stereo and the hi-fi became a stereo system, which showcased those rock albums and vice versa. Production techniques also improved rapidly. The Beatles started out with a three-track machine. By Abbey Road they had a 32-track console to play with. Synthesizers and other electric instruments added new sound textures.
Until the 1960s, FM stations were few in number and mostly were owned by AM stations and just repeated their playlist. Simulcasting was banned in 1966 and the FM stations had to fill up their own air. Innovative stations and DJs started playing whole albums or at least the longer cuts from albums. They sounded better than AM and had much more interesting music, especially after 1970 when Top 40 rock went into the toilet. Without FM and long-playing music only found on albums, rock would probably have died in the 1970s and something else would have taken its place.
We swamped 'em with sheer numbers. The baby boomers were born to rock. They had lots of money to spend on music, concerts, and stereo gear. Fortunes could be made, far huger than anything in the 1950s. The music business was dragged kicking and screaming into rock but they loved the money coming in and cared about nothing else.
Ah, I misunderstood the OP to be asking when rock had been around long enough for some rock to be called “classic” as opposed to contemporary.
My theory is that most genres of music fade away from the popular scene as the people who grew up with it get old and irrelevant. But rock and roll from the sixties and seventies did not fade away. Due to a combination of the shear size of the baby boom generation, and the fact that music that came later really sucked. So for the first time in a long time, older music became a valid and popular genre. They needed a name for it, and Classic Rock hit all the right notes. JMHO.
Bonus discussion question: if an artist from the classic rock era (say, Paul McCarntey or The Eagles) puts out new music today, does that count as Classic Rock?
That’s an interesting question. IME, “classic rock”-format radio stations rarely, if ever, play newer music (say, from the past 25 years) from artists whose earlier music are on their playlists.
For example, Tom Petty kept recording new music all along, but classic rock stations never played his newer stuff; about the newest stuff from him that one might hear on a classic rock station is songs from his 1994 album, “Wildflowers.” Petty put out eight albums after that one (five with the Heartbreakers, two with Mudcrutch, one solo), but I don’t think they ever got any significant airplay on classic-rock stations.
One of the first times I ever felt “old” was the first time I heard 1990s grunge rock (Pearl Jam, specifically) on a classic rock radio station.
When I was a kid in the 1970s and asked clerks for records that were 15-20 years old, they were called “oldies”. And the clerks looked at me like I was nuts. Nobody wanted old crap. Don’t you know everything new is better than everything old? It’s a foundation of marketing, especially to kids.
I first heard the term “classic rock” in the mid-1980s. It seemed to cover rock from the Beatles/Beach Boys era to any bands that were no longer together (or charting).
Fifties rock and roll wasn’t generally lumped in with “classic” rock.
Relevant SDMB thread from a couple years ago:
Is The “Rock Era” Over? If so, when did it end?
According to this article in The Atlantic, the era of rock music ended in 1991.
Exapno Mapcase: Very nice! I look forward to your monograph on robot rock bands.
You poor pitiful fool! We brush aside your feeble attempts at humor!
Start with my article on Servotron.
Chapter 16 of my book indeed reveals to the awe-struck millions more bands of robots rocking, including Compressorhead and Squarepusher. And check slideshow Chapter 16A on my companion site. The penultimate and ante-penultimate slides are videos de la music of robots making a noise joyous.
Did I do my research or did I do my research?
Sha Na Na (the band) performed at Woodstock.
Another nostalgia moment was “Beatlemania” the Broadway show in 1977
In response to the OP: The London Symphony Orchestra started playing rock music orchestrally in 1978 I think, which might be considered a turning point.