First off, ideologically, everything it was selling, Christianity and Zoroastrianism were already selling. Christianity and Zoroastrianism comprised the majority of religious believers in Persia and the eastern Mediterranean by the time Mani began to preach. There is evidence Mani was from an offshoot sect of Judaism, so that would immediately leave his teachings in contention with two of the existing monotheistic religions, as both would see it as just another Messianical rabbi of the week. Think of it was if a tiny sect of Christianity (like Calvinism or something) spawned a prophet, their origins would put many off on principle. Further, it never had a "Constantine" moment where an emperor was converted and enforced it as the state religion, rather, being banned by the Roman Empire as a heresy of/competitor to Christianity. Besides, the ideological and social unrest that Christianity had expanded through had long since been assuaged, and the doctrinal differences to the laity would have been so minor so as not to warrant conversion, especially when the church was becoming so much of a strong authority, in both the East and West. Manichaeism also had a hard time marketing itself to Greeks, who were the original targets of Christian conversion, as their cultural attitudes towards good and evil were much more in line with Christianity (or Christianity was slightly adapted to gain Greek follorwers), in that the dualism didn't sit well with the Greek philosophical tradition.

As for Islam, it spread out of the Arabian peninsula following conquest by some of the greatest military geniuses to ever live, and the ruling class being replaced by Muslims who offered either extra taxes or another brand of monotheism to their subjects made many convert. While Manichaenism did have some success in converting Persians, it didn't have any doctrinal oomph that Christianity or Islam had, with either submission to God and a Muslim Lord or submission to the Church and a Christian Lord.

Iain Gardner and Samuel N. C. Lieu,Manichaean Texts from the Roman Empire (Cambridge: Cambridge University Press, 2004).

Richard C. Foltz, Religions of the Silk Road: Overland Trade and Cultural Exchange from Antiquity to the Fifteenth Century, new ed. (Palgrave Macmillan, 2000).

Neumann, Henry. "Manichaean Tendencies in the History of Philosophy." The Philosophical Review28.5 (1919): 491-510.