This is an incredibly difficult question to answer specifically, after Constantine's conversion and making Christianity the state religion in 324 AD, there were a number of points of interest which may give an inkling to how many polythist remained in rome and surrounding areas.

361 to 363 Religious tolerance and restoration of the Pagan cults declared in Constantinople (11th December 361) by the Pagan emperor Flavius Claudius Julianus. Julianus is also known as Julian the Apostate, he attempted to revitalise the polytheistic religion of the roman empire with a mix of neoplatonic philosophy.

370 Valens orders a tremendous persecution of non-Christian peoples in all the Eastern Empire. In Antioch, among many other non-Christians, the ex-governor Fidustius and the priests Hilarius and Patricius are executed. Tons of books are burnt in the squares of the cities of the Eastern Empire. All the friends of Julianus are persecuted (Orebasius, Sallustius, Pegasius etc.), the philosopher Simonides is burned alive and the philosopher Maximus is decapitated.

380 On 27th February, Christianity becomes the exclusive religion of the Roman Empire by an edict of Emperor Flavius Theodosius, requiring that “all the various nations, which are subject to our clemency and moderation should continue in the profession of that religion, which was delivered to the Romans by the divine Apostle Peter”. Non-christians are called “loathsome, heretics, stupid and blind”. In another edict Theodosius calls “insane” those that do not believe in the christian god and outlaws all disagreements with the Church dogmas. Ambrosius, bishop of Milan, starts destroying all the Pagan Temples of his area. Christian priests lead the mob against the Temple of Goddess Demeter in Eleusis and try to lynch the hierophants Nestorius and Priskus. The 95 year-old hierophant Nestorius, ends the Eleusinian Mysteries and announces the predominance of mental darkness over the human race.

388 Public talks on religious subjects are also outlawed by Theodosius. The old orator Libanius sends his famous Epistle “Pro Templis” to Theodosius, with a hope that the few remaining Hellenic Temples will be respected and spared.

395 Two new edicts (22nd July and 7th August) cause new persecutions against Pagans. Rufinus, the eunuch Prime Minister of emperor Flavius Arcadius directs the hordes of the baptised Goths (led by Alaric) to the country of the Hellenes. Encouraged by Christian monks the barbarians sack and burn many cities (Dion, Delphi, Megara, Corinth, Pheneos, Argos, Nemea, Lycosoura, Sparta, Messene, Phigaleia, Olympia, etc.), slaughter or enslave innumerable gentile Hellenes and burn down all the temples. Among others, they burn down the Eleusinian Sanctuary and burn alive all its priests (including the hierophant of Mithras Hilarius).

415 In Alexandria, Egypt, the Christian mob, urged by the bishop Cyrillus, attacks a few days before the Judaeo-Christian Pascha (Easter) and cuts to pieces the famous and beautiful philosopher Hypatia. The pieces of her body, carried around by the Christian mob through the streets of Alexandria, are finally burned together with her books in a place called Cynaron.

486 More “underground” Pagan priests are discovered, arrested, burlesqued, tortured and executed in Alexandria, Egypt.

529 Justinianus outlaws the Athenian Philosophical Academy and has its property confiscated.

Up until 530 AD it is fairly reasonable to suppose that there may have been underground groups of polytheists in Rome, since the Platonic Academy in Athens was still run by pagans, it can be fairly certain they had substantial funding from tuition fees.

The last last Hellenes in Laconia were reportedly converted before 988 AD, so we can be reasonably certain that there were no polytheists remaining in the large population centre of what was the Roman empire.

Throughout the 370 to 530 AD there were numerous other decrees and orders for the destruction of temples, banning of public and private rituals, even looking at already vandalised pagan statues was outlawed, books from pagan polytheist were piled up in streets and burnt along with decrees against the works of Julian and Porphyry being made on two separate occasions.

It is widely believed that pagan aristocrats remained in the majority till at least the 380s, and continued to be a powerful force well into the 5th century.

The exact date of the last polytheist in Rome will likely never be known, since they slowly disappear out of history all we can gauge their numbers by is the various decrease made against them. If the example of the Platonic philosophers is anything to go by, then the devout polytheist unwilling to convert likely fled as refugees to distant parts of the empire and elsewhere.

On an interesting side note in the early 1800s a British traveller to Eleusis found the locals venerating an ancient statue they said was of “Saint Dimitra [Demeter]” and whose blessings they sought for their fields and crops. The Englishman carried of the statue and sparked a riot.