The short answer is Christianity.
The long answer is it depends what exactly you consider a religion's end. If a religion changes a bit, has it ended? Probably not. If it changes a lot, has it ended? Kind of, but again probably not.
Egyptian religion was not the monolithic entity you learn about in kid's books. Which gods were evil and which just dangerous; which gods were supreme; which gods had relationships with which other gods; what gods were called. All of this changed over thousands of years.
The big change near the end of the BC period was Hellenization. By 30BC, Egypt had been ruled for a considerable time by the Ptolemy dynasty. The original Ptolemy had been one of Alexander the Great's generals (and thus a Greek). When Alexander died and his generals divided his empire, Ptolemy got Egypt.
As foreigners, the Ptolemies were very keen on looking "Egyptian" to their new subjects. But they also wanted to do things the Greek way where possible. In fact, only the very last Ptolemy (Cleopatra) even learned Egyptian. Soon, a nation of Egyptian-speaking peasants, worshipping Egyptian Gods, were ruled by an administrative class of Greek-speaking worshippers of Greek gods.
So, in an attempt to try and ensure Greeks and Egyptians got along, the Ptolemies promoted a number of syncretic Gods; mixes of Egyptian and Greek gods, intended to be something everyone could worship. However, they didn't want to push their subjects too far, so it didn't have a huge effect on the religion of most people in Egypt. That's not to say it was utterly irrelevent, it was popular amongst the upper classes; Pharoah Cleopatra Philopater and Marc Antony held a deification ceremony where Cleopatra was declared the personification of Isis-Aphrodite and Marc Antony as Dionysius-Osiris.
When the whole business with Cleopatra and her alliance with Marc Antony went horribly wrong, with Octavian defeating their forces and them both (eventually) comitting suicide, Rome had the opportunity to take direct control of Egypt. In 30BC, the new "first citizen" Octavian appointed one of his supporters (Gaeus Cornelius Gallus) as the first Prefect of Egypt. These men were from the equestrian (kind of upper-middle class) order, not the Senatorial, and were changed every 3 or 4 years, ensuring no powerful Roman family could rule Egypt independently. All in all, the whole thing was set up to ensure Egypt was firmly under the control of Rome's central government.
With the Romans in charge, Hellenisation was pushed much further, in an attempt to get rid of Egyptian customs. Thus the syncretic Graeco-Egyptian religion was promoted a lot more.
I've already mentioned Isis-Aphrodite and Dionysius-Osiris. Other examples include Hermanubis (Hermes-Anubis, of course) and Serapis (a kind of Osiris-Apep-Zeus-Dionysius figure). All of these predated direct Roman rule, but under the Romans they became much more popular and influential.
In the next 3 centuries, these Graeco-Egyptian deities were the main deities of the upper classes of Egypt. Unfortunately, we don't have much in the way of writing from the lower classes, so it's difficult to tell whether Egyptian peasants stuck to more traditional depictions of "purer" Egyptian deities. But as they were syncretic deities, it's unlikely people saw the two as particular different.
However, through the second and third century some parts of Egypt became centres of Christianity, and in the 4th century when Christianity became fully supported by the state, in the same way the traditional Graeco-Egyptian religion was, it flourished. In the latter half of the 4th century, as Christians became the preferred religion of the Emperors, paganism declined, but it was still legal and supported by the state, and still very widespread. In 380, the Emperor Theodosius stripped pagan temples of all state support. Over the next two decades, he passed more and more anti-pagan laws; banning divination from entrails on pain of death, closing temples, disbanding the Vestal Virgins, making traditional pagan festivals into workdays instead of holidays, getting rid of the altar of victory in the Senate, and often ignoring Christians who attacked pagan temples. Due to this, Christian mobs, often led by monks from the desert (Egypt's desert had long been popular with Christian monks and hermits, all the way back to the 2nd century's "desert fathers") destroyed a number of pagan temples in Alexandria and other Egyptian cities, generally getting away with it.
Paganism was still technically legal under Theodosius; but Roman Paganism was a religion that revolved a lot more around festivals and public rites than belief, and most of the public rites had now been made illegal or at least untenable (because no-one could afford to hold them without state funding; this happens to coincide with a period noted for the reduction in the willingness of rich Romans to fund public ceremonies and works, so even rich pagan noblemen weren't that fussed about paying for the small number of public pagan rites that were still legal. They were more likely to just worship their traditional gods at home). As in Rome, a lot of Egyptians, especially the old nobility, were still not Christians, but Christianity had definitely become the dominant religion.Over the next few hundred years Graeco-Egyptian religion faded away, and by the time of the Arab conquests there's no substantive evidence that anyone in Egypt was still worshipping Ra, Osiris, Isis, etc, even in their "pure" Egyptian form or the syncretic Graeco-Egyptian form.
I cannot answer the first part of this question about when ancient Egyptian religious practices stopped, hopefully someone with a background in the field of Egyptology or the Ancient Near East can offer more insight.
On the second part, there are several modern groups that practice what they understand to be revived versions of ancient Egyptian practice. Most of these would usually be described by scholars as new religious movements or forms of neo-paganism. Much as Wiccan's imagine their linage to go back to ancient Druidic practices and European witchcraft these revived Egyptian religions conceive of themselves as in continuity with ancient practices, though most scholars would question if there was a direct historical connection.
The best studied of these groups is Kemetic Orthodoxy, which was formed in 1988 by Tamara Siuda. Siuda was training to be a Wiccian priestess when she felt that she was contacted by the Egyptian gods while in a trance. She assumed religious leadership of the organization and adopted the title of Nisut, which the organization translates to "The One in Authority." Kemetic Orthodoxy seems primarily organized through the internet, but they also run a temple in Illinois and retreat center in Michigan. In the early 2000s it seemed that Kemetic Orthodoxy had around 200 members.
In San Francisco there is a Temple of Ra and in San José there is a Kemetic Temple. Neither of these organizations is formally affiliated with Kemetic Orthodoxy. Both seem to try to integrate ancient Egyptian texts and rituals into their worship.
The Temple of Set might also be regarded as inspired by ancient Egyptian religion. The organization was founded by Michael Aquino in 1975 after he separated from Anton LeVey's Church of Satan. Setians worship the ancient Egyptian God Set, many of them believing him to be the true name of Satan. They believe Set to be a rebellious, free-spirited deity.
Recommended Readings:
Harrison, Paul. Profane Egyptologists : The Modern Revival of Ancient Egyptian Religion. London, England: Routledge, 2017. .
Krogh, Marilyn C., and Brooke Ashley Pillifant. “Kemetic Orthodoxy: Ancient Egyptian Religion on the Internet — A Research Note.” Sociology of Religion 65, no. 2 (July 1, 2004): 167–75. https://doi.org/10.2307/3712405.
Petersen, Jesper Aagaard. Contemporary Religious Satanism: A Critical Anthology. Farnham, England: Ashgate Publishing, Ltd., 2009.