Sometimes, the threshold is attitude, or innovation that carries on a while. Still, a fairly finite set of parameters.
Steel lugged bikes simply generated a following that exists today, long after the "mainstream" bike has gone from steel to aluminum to carbon. Builders still build them, buyers still buy them, and people still ride them. To say they're not classic is difficult to support, when many are going for $2500 or more, frame only, when new. The "basics" of them have not changed a whole lot. Go to a classic show, though, and it's very easy to see the differences in "classicity" between a 1933 Frejus and a 1974 Super Corsa and a 1989 Parmount OS. I'm sure there are differences between riders on different continents, as well. Is a Trek 760 a classic in Europe, and is a Moser Leader a classic in Boston? Not sure.
Some look at the components, from rod brakes, hand-shifted chains, and rudimentary engineering through to the now "classic" downtube indexed shifting. I put the latter in the classic "looks" department. Some are brand-oriented, some are not.
Then, there are some carbons considered classics, from the carbon/lugged models like the Line Seeker to the previously mentioned Specialized models, and include Treks, Alans, and other models. These have a classic look, and some actually ride fairly well, but not all. The carbon turning point, to me an many others, came when some Aegis employees split from Maine and headed west, generated some capital, and unleashed the Kestrel 200 series models. They are becoming "classics" in their own right, both for age and a design which was ahead of it's time and has held up pretty well for 29 years or so. Roccobike's Lemond Maillot Juene is often considered an "instant classic," and fits the narrow definition I have in mind.
Other classics are either unique, or famous, or infamous, overhyped, underhyped, or just plain superb in their own right. It takes all kinds. Japan's cycling culture has trends that seem to come and go very quickly, and would a classic one day be passe the next, and if so, be eliminated from being classic?
I suppose, when people make these kinds of choices, there will be less consensus than grudging give and take.