It is probably better to think of Mithraism as already part of a major religion (really the major religion) in the Roman Empire than a contender. Something that's very clear from observing questions on this sub, and portrayals in pop culture, is that people in the modern world, dominated by monolithic "this is the true way" religions, really struggle to picture ancient polytheism. Ancient polytheists tended to see additional gods as entirely compatible with their existing pantheons. Maybe they were the same deities going by different names, or maybe they were new, previously unknown gods who could now be worshipped. Unless their believers, for example Jews and Christians, demanded monotheistic adherence to that god alone, it was easy enough to add new gods and their mythology into the existing belief structure.

In the 1st Century BCE, Marcus Terentius Varro described Roman and Hellenistic theology as composed of three parts (the so-called tria genre theologiae) in his Antiquities of Human and Divine Things. He did not invent the concept, but famously described it quite succinctly. In reverse order they were:

• Civile - Civil religion practiced in public and sponsored by the state. I suspect this is what a lot of people imagine when thinking of ancient religion practice. It includes public holidays, sacrifices, grandiose temples, and other obvious public displays.
• Physikon - In the broadest definition of "physics," as in the whole study of the natural world. This was the idea of religiously or philosophically trying to understand the nature and behavior of divine beings, both as individuals and their actions in nature/human life.
• Mythikon - Varro describes this as "all the things which are ascribed to the gods." It includes both the stories of mythology but also the personal practices relating to those stories.

Mythikon theology is simultaneously the best and worst understood part of Varro's theologiae today. Many modern people immediately know of at least a few ancient stories about the gods. However, the actual day-to-day rituals of personal religion not sponsored by the state remain fairly obscure. This is due, in part, to the nature of those rituals as the realm of "Mystery Cults." The Mithraic Mysteries were just one of such cults. The other extremely famous example, routed in Archaic Athens, is the Eleusinian Mysteries, dedicated to the goddess Demeter. A core part of the Mysteries, regardless of which cult you're talking about, was that their actual practices and rites were known only to initiates in the cult and deliberately kept secret beyond the mythology (ie stories) they were based on. This served the dual purpose of attracting people who wanted to know into the cult, and of keeping their rites from being disrupted or despoiled by those who might attempt poor imitations and incur divine disfavor.

The Mystery Cults were a way to personally participate in Mythikon theology alongside the other two genre. Many of them started out as local practices that spread and set up branches during the Roman imperial period. Mithraism was particularly widespread, and thus apparently popular, with large "Mithraeums" found across the whole breadth of the Empire.

I should not here that "cult" in the ancient polytheistic sense does not mean a shady group of scammers or loons awaiting some imminent apocalypse or reveal of conspiratorial secrets. It's simply the word we use to describe the dedicated group of adherence for a particular temple or deity because Latin cultus is how they described themselves. It literally means "a thing that is worshipped/adhered to."

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But how would so little be known about a cult supposedly popular within the military? Wouldn’t minorities and spies/ within/around Rome have notes?

As Mysteries go, Mithraism is actually extremely well documented, another testament to its popularity. By the very nature of their structure, the specific details of any Mystery were kept a secret. They had texts, but they were for members only. Other people heard about some of them, and what they heard did get written down, but the records of minority groups and spies aren't exactly the sort of thing that get copied and spread around. The vast, vast majority of ancient writing has not survived to the present day. Works of particularly impressive literature, long-lasting and influential philosophical schools, and the occasional seminal history are the only ones that really merited perpetual manuscript traditions over the last 1700+ years. A shocking number of key historians and historical details used by modern historians are only known because they are quoted, summarized, and referenced in other works.

Mithraism in particular got, and continues to receive, special attention because of its similarities (both real and perceived) to another secretive cult that was spreading through the Empire around the same time. Which brings me to:

was there a specific event historians point at and go this is where Mithraism became regulated to a footnote?

That'd be Christianity. Much like the Mystery Cults, early Christianity was a loosely structured religion that kept the details exclusive to its members, and because they were the words of the time, Christianity used much of the same terminology to describe religion as the Mysteries. Mithraism carried the additional connections of a divine figure contrasting divinity with mundane mortality, was worshiped through a feast replicating one of his great deeds, and whose birth was central to his mythology. In more recent times, people have also drawn attention to the fact that Mithra's birth was celebrated on December 25, but by all indications this is largely unrelated to how later Christianity determined a date for Christmas.

Similarities between Christianity and Mithraism, and the Mystery Cults in general, were noted very early on. In the 2nd Century, the Christian apologist, Justin Martyr, wrote:

Jesus took bread, and when He had given thanks, said, "This do ye in remembrance of Me, this is My body;" and that, after the same manner, having taken the cup and given thanks, He said, "This is My blood;" and gave it to them alone. Which the wicked devils have imitated in the mysteries of Mithras, commanding the same thing to be done. For, that bread and a cup of water are placed with certain incantations in the mystic rites of one who is being initiated, you either know or can learn. (First Apology, 66)

Had Christianity died out, the structure of the early church would likely have left its rites just as obscure as the pagan Mysteries. As it stands, the early structure and exact practices of Christianity is a matter of great debate as scholars try to pick out details from oblique references in the New Testament and writings from early Church Fathers. Instead, Christianity blossomed and gained traction among the highest rungs of Roman society.

Beginning in the mid-4th Century, non-Christian beliefs in the Roman Empire faced escalating persecution. How much more Constantine I did for Mythikon theology beyond giving Christians preferential treatment is up for debate, but he did defund Pagan temples, essentially gutting Civile theology at its core. His successors explicitly targeted non-Christian rituals for decades, beginning with a ban on Pagan sacrifices and divination under Constantius II, Pagan practices were under escalating pressure for decades (aside from the brief Pagan restoration by Emperor Julian "the Apostate"). The reign of Theodosius I was the final straw. Every remaining piece of state sponsored polytheism was abolished, visiting Pagan temples was forbidden, and divination and "witchcraft" were made capital crimes. The latter could essentially cover any ritual worship of non-Christian gods. When he became sole Emperor in 392, Theodosius authorized the destruction of pagan shrines across the empire.

Under threat of death and imperial persecution, most people just converted and holdouts couldn't openly operate their shrines or solicit new members for the Mysteries. Pagan cults did try to keep going, which is demonstrated by repeated Imperial and Papal decrees targeting their shrines and practices, but by the mid-6th Century they were functionally extinct.

Plenty of new research has occurred in the last 70 years. Mithras by Andrew Fear is a brand new survey of some of the latest information. Encyclopaedia Iranica also offers a relatively modern (2002) academic overview of the basics.