I would certainly contest the claim that Zoroastrianism was unable to resist the spread of those faiths. Its decline came as a result of the Arab conquests and gradual conversion for social benefits, not some fanatical evangelism. In fact, it had been able to resist Christianity quite well (The conversion by Armenian elites, which had a peculiar political context, notwithstanding) while accomodating Christian miniorities in its domains. Manichaeism was banished to the fringes of the Sasanian Empire at the high priest Kerdir's zenith of power, and thrived not in the West Iranian heartland but in the East and Northeast, regions with long traditions of Buddhist, Zoroastrian and Hellenic syncretism where Manichaeism fit in quite naturally.

Moreover, it is at minimum misleading to call Zoroastrianism "monotheistic". Ahura Mazda is the supreme being and uncreated creator, but in practice many different divinities are worshipped in Zoroastrianism, generally understood to be created from the perfect substance of Ahura Mazda. Some traditions hold Mithra and Apam Napat to be both created by and equal to Ahura Mazda in stature. Monotheism is as a rule better understood as a statement of doctrine than a description of a religion (e.g., the Trinity in Christianity is thought in traditional Muslim teachings to violate the "oneness" or indivisibility of God that is a core idea of Islamic monotheism). The emphasis on monotheism that exists today in some Zoroastrian groups is just 200 or so years old and a consequence of reactions to Christian missionaries and interactions with Western scholars who applied a Biblical framework in their understanding of Zoroastrianism.

It is correct to call Zoroastrianism dualistic, but one must take care to distinguish between two equally important dualisms - good and evil, as well as spiritual and material. The spiritual and material are both at heart good, but only the spiritual is incorruptible. It seems, for instance, that the bones were thought to be the "perfect" core of the human body, while the flesh was weak and corruptible.

But still, this doesn't really answer your underlying question of what enabled the rapid growth of certain religions. I think the most compelling overarchingexplanation is to look at what all of those have in common: Hellenic influence. The Hellenic part of the world, in which the Arsacid/Parthian Empire can essentially be included, had certain common aesthetics, modes of thinking, etc. Moreover, there had been at work around the introduction of Christianity many centuries of syncretic and interfaith flourishings, creating a world that was not just diverse, but contained certain common denominators. Perhaps we shouldn't see these movements as too sudden, but rather as the natural continuation of cultural processes that were already underway.