I've crossposted this to /r/AcademicBiblical; however, you might also have some luck at /r/ChristianUniversalism--even though some of the people over there are kind of my arch-enemies (because of what I consider to be some pretty uncritical, ahistorical views).

Although somewhat polyvalent--and perhaps leading to some significant confusion among scholars and laymen alike--apokatastasis is a convenient sort of technical term that signifies the (patristic) notion of universal reconciliation. (For an illustration of its polyvalence, just take a look at "the complexity of the notions of apokatastasis that Clement [of Alexandria] received, as they were already present in various traditions with which he was acquainted"--quoted/taken from Ramelli 2013:119-20.)

If you're interested in the most current scholarly treatment of the issue, Ilaria Ramelli has written an absolutely magisterial work on it which will surely be the standard work for many decades (The Christian Doctrine of Apokatastasis: A Critical Assessment from the New Testament to Eriugena).

In her first chapter, she writes that 'the group of writings stemming from the second century CE and collectively labelled “Apostolic Fathers,” the doctrine of apokatastasis as eschatological universal restoration appears to be missing'; however she mentions several 2nd century theologians/authors--Justin Martyr, Tatian, Theophilus of Antioch--who might have some hints in that direction: e.g. she mentions that we can find, in Justin, "the language of apokatastasis and its application to an eschatological context, moreover with strongly inclusive elements." She discusses this people as catalysts for development in some of the notions that the more well-known universalists would adopt, even if they themselves not not universalists.

The big universalist names, however, are Clement of Alexandria, Origen and Gregory of Nyssa; and various others enlisted for support like Didymus the Blind, Evagrius, etc.--and some others tangentially mentioned, or claimed for partial support (e.g. Cyril of Jerusalem; sometimes even Eusebius, etc.).

I certainly haven't worked through all of Ramelli's nearly 1,000 page tome; so perhaps comment should be reserve until such time. I'll let you be the judge of these separate individuals, if you look into them--though note also that some have challenged some of the more 'monolithic' views of their universalism. Some of Origen's statements seem to be hard to reconcile with each other, even when accounting for theological development (the same might be said for Paul himself, among others); and here's a recent paper on Gregory of Nyssa that challenges some common views held about his theology. Even the Wiki page for apokatastasis now mentions this prominently.

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Unfortunately, I can't speak much to its "disappearance," if this is even the right term for it. A starting point might be the "condemnation" of Origen; however, as Ramelli argues,

The so-called “condemnation of Origen” by “the Church” in the sixth century probably never occurred proper, and even if it occurred it did so only as a result of a long series of misunderstandings, when the anthropological, eschatological, and psychological questions were no longer felt as open to investigation—as Origen and still Nazianzen considered them—, but dogmatically established. The aforementioned condemnation was in fact a condemnation, not at all of Origen, but rather of a late and exasperated form of Origenism; moreover, it was mainly wanted by emperor Justinian—or better his counsellors, given that he was not a theologian—and only partially, or even not at all, ratified by ecclesiastical representatives.

However, Origen (or perceived Origenism)--and along with him, some various notions of apokatastasis--did suffer during this time (~6th century; cf. the fifth ecumenical council and its anathemas). Ramelli writes that "One problem is that later Christian authors considered the aforementioned anathemas as referring to Origen; so, extraneous theories were ascribed to him."

I imagine we just see after this more and more criticism or whitewashing of earlier 'universalist' figures around this time. Ramelli continues that later manuscripts of Gregory of Nyssa's writing "bristle with interpolations and glosses concerned with explaining that Gregory did not support the theory of apokatastasi," and notes that "Germanus of Constantinople, in the eighth century, even claimed that Gregory’s works were interpolated by heretics who ascribed Origen’s ideas to Gregory." She also discusses something that I think may show why universalism continued to have a legacy, even if it became marginalized:

A monk has asked [the 6th century ascetic Barsanuphius] how it is that Origen’s doctrine, especially that of apokatastasis, was supported by orthodox authors, and even saints, such as the Cappadocians. Barsanuphius, far from trying to deny that the Cappadocians supported the doctrine of apokatastasis, simply observes that even saints can have a limited understanding of the mysteries of God and can be wrong.

Presumably not everyone was persuaded that these holy men had such a "limited understanding" (as many liberal Christians today are persuaded that the New Testament itself teaches universalism!).

FWIW though, Ramelli continues to discuss univeralist-leaning theologians/authors until about the 9th century. I'm not sure why why she stopped there; no reason is given (as far as I've read). Maybe she just ran out of space--almost 1,000 pages into it.