Defining the end point
The civilisation of ancient Egypt can be traced back in recognisable form to around 3000 BC. It was to endure for over three millennia and it is perhaps the most instantly recognisable of all ancient cultures today. The question of how it came to an end is a perennially popular one, but actually quite difficult to answer, as it is by no means agreed as to what constitutes 'the end' of Egypt as an ancient civilisation.
...the demise of the hieroglyphs was a manifestation of the decline and fall of the ancient religion...
Is it the definitive end of native Egyptian rule (at least until the 20th century)? In this case the answer would be the flight of King Nectanebo II in 342 BC. Is it Egypt's absorption into the Roman Empire in 30 BC? Or the last appearance of the ancient hieroglyphic script just before AD 400? Or the closure of the last pagan temples in the sixth century?
In many ways the last suggestion is perhaps the most appropriate, as in all the other cases, the core religious and artistic values of the country continued on, albeit increasingly debased and under pressure. However, the demise of the hieroglyphs was a manifestation of the decline and fall of the ancient religion in the face of Christianity, itself ultimately to be supplanted by Islam.
Signs of trouble
...this falling behind in military technology was certainly a contributory factor in the coming decline.
One of the differences between their armies was that while the Egyptians were armed with weapons of bronze, the Hittites had access to a new material - iron. Although they had ample reserves of copper (the key component of bronze) within their boundaries, the Egyptians lacked sources of the far more effective metal. While this was by no means a decisive issue, this falling behind in military technology was certainly a contributory factor in the coming decline.
There were also cracks appearing in the unity of the Egyptian state, and its cohesion was threatened by a short-lived secession of the southern part of the country under the rebel king Amenmesse around 1200 BC, by the murder of Ramesses III in 1153 BC, and by civil war in the far south around 1080 to 1070 BC. Economic crises, raids by foreign bandits, and an orgy of tomb-robbing, during which many of the graves of the ancient pharaohs were looted, accompanied these events.
The net result was that for the century from 1070 BC onwards, under the 21st Dynasty, Egypt was split in two, the north ruled by the pharaoh, based in the new city of Tanis in the north-east of the country, and the south by the High Priest of Amun at Thebes (modern Luxor). The High Priests nominally owed allegiance to the king, but in practice they comprised an independent line of hereditary rulers, whose status was not solely religious, as they also held the title of Army Leader, making their regime probably more of a military dictatorship than a Taliban-style theocracy.
Wars
Although of foreign - Libyan - origins, he brought the south back under central control by the expedient of supplanting the old High Priestly family with his own son, and pursued an aggressive foreign policy, including military campaigns in Palestine, during one of which Jerusalem was sacked.
However, within a century, the country had split again, with Thebes now ruled not by High Priests, but by its very own line of pharaohs, the 23rd Dynasty, running in parallel with the Tanite (based in Tanis) northern king.
This decline coincided with the rise of a power to the south of Egypt in Nubia...
The Theban kings soon found themselves embroiled in a long-running civil war, while in the north a number of semi-independent principalities grew up, all together sapping the strength of the country as a whole. This decline coincided with the rise of a power to the south of Egypt in Nubia - spanning the borders of the modern states of Egypt and Sudan. Long a colony of Egypt, Nubia now had rulers (the 25th Dynasty) who regarded themselves as ideologically the heirs of the ancient culture of Egypt, and as such they became overlords first of Thebes, and then took over the whole of Egypt, becoming pharaohs of a united kingdom of Egypt and Nubia around 720 BC.
Invasion
Egypt thus fell easy prey to the expanding Persian empire in 525 BC...
Although this was apparently a time of peace and well-being, the Assyrian invasion indicated that Egypt's fate was now firmly tied in with the rest of the eastern Mediterranean world, in which it struggled to maintain its economic and military position. Indeed, the army now relied heavily on foreign - especially Greek - mercenaries, rather than the native Egyptians of the country's glory days.
Egypt thus fell easy prey to the expanding Persian empire in 525 BC, remaining under their dominion for over a century. National rule was revived between 404 and 342 BC, but the various regimes (the 28th, 29th and 30th dynasties) were riven by in-fighting, and the Persians reasserted their power in 342 BC. Egypt was seized by Alexander the Great in 332 BC, but regained independence at the break-up of his empire in 310 BC.
However, the new ruler, Ptolemy I, was a Macedonian Greek, and the ruling class of the state was now foreign, running the country as part of the Ptolemaic kings' wider Mediterranean agendas. The ancient religion and culture were supported and new temples built, but the dominant culture was now increasingly European, with Greek becoming the language of state.
A mere province
While the Ptolemies' support for traditional culture was maintained through a programme of temple-building, in which the Roman emperors were depicted as pharaohs, the infiltration of foreign philosophical and religious ideas continued apace. In particular, Christianity took early root in Egypt, doubtless aided by its many similarities to the popular cult of Osiris and Isis, which also featured an unjustly killed divine figure who was resurrected to provide humans with a guarantee of eternal life.
Egypt now became a mere province, with its primary goal to provide grain for the rest of the empire.
The association of the ancient hieroglyphic writing system with the old religion, together with the wide currency of the Greek language in Roman Egypt, led to the Christians beginning to write the native Egyptian language in an augmented version of the Greek alphabet. The old art style was also tainted with paganism, and so was also replaced by a style derived from outside, thus further eating away at key parts of the ancient Egyptian civilisation.
End of the old ways
By the fourth century AD, the old ways were largely concentrated in the south of Egypt and the remote Western Desert oasis of Siwa. Perhaps the most important sanctuaries were concentrated on the temple-island of Philae, on what was then the country's southern border. It was there that last inscription in hieroglyphs was made in 394 AD, as well as the final example of its hand-written form, demotic, in 452 AD, and it was here that the last pagan sanctuaries in the Nile Valley were forcibly closed in 553 AD.
All that survived was the Egyptian language itself, fundamentally the same as that spoken by the first pharaohs...
By then, Egypt was a Christian country which now rejected much of its heritage as indefensibly pagan. All that survived was the Egyptian language itself, fundamentally the same as that spoken by the first pharaohs, three-and-a-half millennia earlier. And even that was not to endure, since with the Arab invasion in 640, Arabic began to displace it, until by the 16th century it was essentially restricted to Church liturgy. But it still clung to life, and its survival was to be a key tool in the decipherment of the ancient hieroglyphs in the 19th century.
Although now reflecting a dead culture, the image of ancient Egypt continued to endure, through the Bible and the works of ancient and medieval travellers, to be revived in the years that followed the invasion of Egypt by Napoleon Bonaparte in 1798, and the decipherment of the hieroglyphs in the 1820s. As a field for scholarly research, or simply a holiday destination, Egypt remains imprinted on the world's consciousness in a way hardly equalled by any other ancient society, centuries after its culture apparently vanished from the earth.