To my knowlege one of the last pieces of evidence for the practise of an Ancient Egyptian cult comes not from Egypt itself but from Nubia. The peoples that had settled there in Late Antiquity (Nobatae, Blemmyes etc.) were still mostly pagan up to the 5th and 6th century A.D. They were periodically raiding the south of Roman Egypt until the general Maximinus could force them to sign a peace treaty in 453 A.D. As a part of that agreement the Nobatae and Blemmyes were allowed to access the sanctuary of Isis on the isle of Philae in southern Egypt and to take the cult statue of the goddess to their homeland once a year (Priscus, frg. 27). The temple was finally closed by the emperor Justinian between 535 and 538 A.D. Around the same time he and his wife were sending christian missionaries into Nubia.

See: R. Dann, The Archaeology of Late Antique Sudan. Aesthetics and identity in the Royal X-Group tombs at Qustul and Ballana (2009) p. 19; D. A. Welsby, The Medieval Kingdoms of Nubia. Pagans, Christians and Muslims along the Middle Nile (2002)

To piggyback on OP's question, what kind of definition is used for dying out when talking about religions, since presumably you can never be sure if a religion really has zero adherents?

There seems to be some evidence that Egyptian temple cult was already in decline in imperial times. After Augustus conquered Egypt he invested heavily in the building, enlarging and repairing of Egytian temples. Future Roman emperors would continue to do so but on a much smaller scale. In the 3rd century A.D. this activity seems to have stopped at all. At the end of the century even the once so important temple of Luxor was converted into a military camp. Unfortunately that doesn't really say much about the religious practice of the Egyptian population at large.

See: R. S. Bagnall, Egypt in late antiquity (1993)