Manichaeism was a classical religion, roughly contemporaneous (plus a few hundred years) with Christianity founded by the prophet Mani in Sassanid Persia, incorporating elements of Zoroastrian, Christian, and Buddhist (among others) beliefs into a syncretic and highly gnostic whole. It was able to gain a number of converts and spread throughout Eurasia, from China to Britain, but ultimately declined and fell under the persecution of orthodox Christianity, Zoroastrianism, and, eventually, Islam in the west and the state in China (similar to the Nestorian church). Today it's largely a historical curiosity which is probably best known as the religion St. Augustine of Hippo followed before his conversion to orthodox Christianity.
So, obviously, it sparks the question of what the world would look like if it had been much more successful, remaining a major world religion to this day, perhaps even supplanting Christianity as the largest religion of the world (that would be reaching a bit). Thus the post, which asks just that; what factors would be needed for Manichaeism to be more successful (not necessarily to the "replacing orthodox Christianity" level, just so that it survives as a reasonably important world religion to the modern day)?
The most obvious factor needed seems, to me, to be a culturally and politically influential patron state, just as Christianity benefited from the support of the Roman Empire, Islam from the Caliphate, and Buddhism from the Mauryan Empire. The most obvious candidate is the state in which it arose, Sassanid Persia, although there's a problem in that the Sassanids were quite Zoroastrian although generally tolerant of other religions (from my admittedly brief reading). Perhaps this can be worked around, however? If the Sassanids are converted, at least the major state apparatus, then it seems to me that you could have a solid Manichee community centered around Persia, with strong influences in Central Asia, Arabia, and other areas linked to Persian trade routes, and smaller communities farther afield (much like Christianity relative to the Roman Empire).