From what I have read, Arianism seems to have had a quite strong popular and political following well into the mid-first millenium: How did it collapse in face of other religions or sects?
The Decline of Arianism falls into three parts, which I will call ‘Arianism Proper’, ‘Pseudo-Arianism’ and ‘Extra-Imperial Arianism’.
By ‘Arianism Proper’ I mean the set of beliefs associated with Arius and his followers. Arius very clearly considered Jesus to be a created being, a mediatorial figure between God and Creation, and like us in every way. It has been typical to consider Arius’ theological rationale the desire to preserve the uniqueness and soleness of God the Father, but Gregg and Groh make a good case that the main thrust of Arian doctrine was actually focused on salvation. The theology of Arius relating to Jesus was necessary so that we could become like him. Arius was condemned at the Council of Nicaea, in 325. This was the first ‘ecumenical’ council though most of the ecumenical councils were composed of a majority of Eastern bishops. This was the main purpose of the council. After the council Arius was exiled, and continued for some time to have a minor following. Constantine wanted to rehabilitate Arius, and in 335 the Synod of Jerusalem restored Arius to communion. However, Nicaea effectively ended Arianism proper as a theological option.
I call this Arianism proper, because what follows in the 4th century is no longer called ‘Arianism’ in the historical circles I read and write in. What you get is a large number of bishops and churches aren’t very happy with the Creed of Nicaea, and aren’t happy to call Jesus “of the same substance” with the Father. So I would rather call this phase ‘Pseudo-Arianism’. A lot of our history of this period has been influenced by Athanasius, who started a polemical practice of calling his opponents ‘Arians’ in order to taint them by association. Constantine dies in 337 and Constntius II becomes emperor in the East, and from 350 over the whole Empire. He is favourable to the anti-Nicene bishops, which at this time is most of the church of the Eastern Empire. Their views are not as extreme as Arius, though there are some theological similarities. You first get the emergence of a group who would rather say that the Son is “like the Father in substance” (Homoiousian), before you get a group from 357/359 saying that the Son is “like the Father” (Homoian), and refusing to talk about “substance” or “being” at all. And from the early 360s you have a radical group saying that the Son is “of a different substance” to the Father (Anomoian or Heteroousian). Both theological debate and changes in Emperors leads up to 380 and 381. On the one hand Theodosius I, (Emperor 379-395) is firmly in favour of the (now) Orthodox position, backing “of the same substance”. On the other, particularly the efforts of Basil the Great, Gregory of Nyssa, and Gregory of Nazianzus, have managed to sway a majority to accept Nicaea and formulate Trinitarian theology along those lines. So the 2nd ecumenical council of Constantinople in 381 ends, within the empire all forms of so-called Arianism. They are no longer allowed to use church buildings, and not allowed to meet within the city. Their power is broken.
But there is a third strand. Ulfilas was a Goth, or possibly half-Goth, who was ordained by Eusebius of Nicomedia, a leading figure among the non-Nicenes. And Ulfilas went as a missionary back to the Goths. He devised the alphabet for the Gothic language, and translated the Bible into Gothic. His mission was successful, and so many Goths were converted to an ‘Arian’ version of Christianity. Conversion efforts among other Germanic tribes also followed along these Homoiousian lines. In the case of the Goths, this kind of Arianism persists until the Third Council of Toledo in 589 where the Spanish Goths (i.e Visigoths) embraced the orthodox position. Those Goths left in Italy, the Ostrogoths, were displaced in the mid 6th century, settling in modern Austria. At this time it is really the Franks that emerge as the major power in central western Europe, and they are already in the Catholic fold.