Frankly, any question of "When did ____ finally die out?" is very hard to give a concrete answer to for a couple reasons you might imagine, not least of which because illicit groups would, of course, prefer to keep their existence secret.

Officially, Greco-Roman polytheism died on 381 AD, when Theodosius I rolled out his aptly named "Theodosian decrees" backed by a strong campaign of enforcement to essentially ban all practices of paganism and criminalize such worship. This was an all-encompassing campaign that dismantled pagan holidays, made temples forbidden ground, arrested magistrates that refused to enforce the laws. Likewise, Western Emperor Gratian codified an end to the tolerance allowed in his half of the empire and rolled out a similar campaign of dismantlement and confiscation. Gratian would abdicate his title of Pontifex Maximus to make it clear to his detractors that he had no further interest in respecting the old practices. In 392 Theodosius became emperor of all of the Roman Empire, and would punctuate his campaign by extinguishing the Sacred Fire of Vesta and disbanding her virgins. It is generally believed he suppressed the Olympic Games, with their last celebration occurring in 393. I am simply scratching the surface of a major discussion into the christianization of Rome (and would be happy to answer follow-up questions you may have on this) but I'll provide some good sources for further reading at the end of this post. I should also note that this is not the moment where the decline began either, arguably since the conversion of Constantine I and his Edict of Milan in 313 the wheels started turning and for the most part, as new Christian communities formed and grew, the old pagan ones declined until actively suppressed.

Of course, just because the Emperor says "stop it" doesn't mean people do, generally we believe the practices likely continued in more rural and remote ends of the empire into the earlier Middle Ages. There remain two major, written examples of pagan beliefs that made it beyond the period of suppression. The first is recorded in the life of the Christian Saint Benedict of Nursia, who discovered a temple and grove to Apollo at Monte Cassino, and had the altar broken and the grove razed, forcefully converting the temple into a chapel in 529. Lasting far longer would be the Maniots, known as the last inhabitants of Greece to be openly pagan. This is likely because the Mani peninsula is extremely mountainous, forbidding the forcible conversions that subsumed most of the reaches of the empire from feasibly striking them. We know pagan practices continued until sometime in the 9th century when they were fully Christianized. Whether they were truly the final practitioners of the religion, no one can really say, but they are, at the least, the last recorded practitioners. 804 is the last date where paganism in Mani is explicitly mentioned (when Saint Tarasios failed his forced conversion attempt) but Constantine VII would write that "up to the present time are termed Hellenes by the local inhabitants on account of their being in olden times idolaters and worshippers of idols like the ancient Greeks, and who were baptized and became Christians in the reign of the glorious Basil" implying they had been converted by his reign (913-959).

Sources & Further Reading:

Harries, Jill, and I. N. Wood. The Theodosian Code: Studies in the Imperial Law of Late Antiquity. Bristol: Bristol Classical, 2010.

Trombley, Frank R. Hellenic Religion and Christianization c. 370 - 529. Vol. I. Leiden: Brill, 1993.

Gregory, Timothy E. "The Survival of Paganism in Christian Greece: A Critical Essay." The American Journal of Philology 107, no. 2 (1986): 229-42. Accessed October 13, 2020. doi:10.2307/294605.

Greenhalgh, Peter, and Edward Eliopoulos. Deep into Mani: Journey to the Southern Tip of Greece. London: Faber and Faber, 1986.