I think the explanation here is more cultural than intellectual. From the late fourth century BC onward, the study of philosophy had been an acceptable pursuit for wealthy Greeks (and, later, Romans) of the leisure class. Whatever joys the life of the mind may have held, by adopting the role of 'philosopher,' men might hope to find patronage in a royal court, or earn the respect of their fellow citizens at home. The third century Menedemus of Eretria, who, because of his reputation as a philosopher, was chosen by the Eretrians to be their ambassador to Macedon, Egypt, and other kingdoms, is a nice example of the sort of worldly benefits the philosophical life might grant its practitioners.

Over the course of the Hellenistic period, philosophy became extremely popular, with the result that there were an astonishing variety of schools, including some famous and long-enduring ones (Cynicism, Stoicism, Epicureanism) and some that died out within a century or so of their birth (Cyrinicism, or Menedemus' own "Eretrian" school). These 'schools' ought to be seen not as institutions or even bodies of knowledge, but as networks of individuals, with successful philosophers attracting students who make use of their master's reputation to attract pupils in turn.

As philosophy increased in popularity, a basic familiarity with it became part of the cultural capital of the Mediterranean elite. Perhaps because philosophy became so deeply ingrained in upper class education, by the second century AD, less emphasis is placed upon the particular intellectual network ('school') in which one was taught. The philosopher is defined more by his characteristic behaviors than by his particular doctrine. Take, for example, the apologia of Apuleius, a later second century work purporting to be Apuleius' defense speech in a trial for witchcraft. Apuleius' defense revolves around portraying himself as a philosopher. But he seems to have little regard for the distinctions between philosophical schools. At points he espouses Platonic doctrines, but at other points he admits to buying weird fish from local fishermen and dissecting them. Such empirical observations of the natural world are part of the Aristotelian school: Plato and his immediate disciples, with their world of abstract forms, wouldn't be caught dead poking around inside a fish. Indeed, if Apuleius' work were the only survival of ancient philosophy, we would have no idea Plato and Aristotle ever disagreed on anything. As Apuleius continues, he acknowledges that he has a household shrine with tiny idols and sacred emblems hidden under handkerchiefs. These, he explains, are from the many mystery cults he was been initiated into, and are covered so that the uninitiated cannot see them. Serially joining mystery cults is a tenet of no Hellenistic philosophical school. But for Apuleius and his audience, piety and the possession of secret knowledge are central tenets of the philosopher.

We can see the same thing going on in Philostratus' Life of Apollonius of Tyana. Apollonius would have lived in the first century AD, but Philostratus' biography is from the early third century. Apollonius was, notionally, an adherent to the philosophical school of Neo-Pythagoreanism. But little in Philostratus' deals with what this adherence meant from an intellectual perspective. Instead, Apollonius casts out demons. He travels to India and visits wizards who live in a floating castle. He has a deep and special relationship with the gods (at one point he goes into a scared cave and emerges a few days later from another cave hundreds of miles away, with a book of philosophy given to him by a god of the underworld. He gives sound advice to a virtuous ruler (Vespasian), and speaks truth to a tyrannical one (Domitian). Like Apuleius, he is defined by his secret knowledge, especially of the divine, and not by doctrinal purity. Its not that Philostratus is incapable of following intellectual networks: in his Lives of the Sophists he traces the intellectual pedigree of dozens of orators, showing how they were all connected in various schools. But when it comes to philosophy, such networks have come to matter less than a general conception of the 'philosopher' as wise and pious man.

Thus, finally, on to Neo-Platonism. Neo-Platonism inherited the idea of the philosopher that developed in the second century. Looking at Porphyry's Life of Plotinus (one of the founding figures of Neo-Platonism), we discover that Plotinus was a prolific writer. But despite the moniker "Neo-Platonic," his ideas did not fit neatly into the school of Platonism, being rather a syncretism of Platonic, Pythagorean, and other schools. As an author, Porphyry is still very much interested in the intellectual network of Plotinus (indeed, the biography is really an excuse to explain how close to the great man he really was). But the way in which Porphyry justifies caring about Plotinus is, once more, through his connection to the divine. Thus we are told that Plotinus once met an Egyptian priest at the temple of Isis in Rome who tried to summon forth Plotinus' daemon (guardian spirit) and discovered that it was a full-fledged god. After Plotinus' death, one of his disciples visited the oracle of Apollo at Delphi, where the god (supposedly) recited an extremely dense poem, the upshot of which was to proclaim Plotinus divine. Knowledge of the divine and the arcane is what gives Plotinus his chops. As Christianity gains currency throughout the empire, the centrality of divine knowledge to pagan philosophers will only become more entrenched.