Simple. It didn't. The Egyptian state completely collapsed not once, not twice, but thrice in the Pharaonic period. Egyptologists refer to the periods following these collapses as the First, Second, and Third Intermediate Periods because they occurred between the Old Kingdom, Middle Kingdom, New Kingdom, and Late Period. The First was caused by the power grabs of several regional nomarchs (similar to governors in the United States), leading to a massive decentralization of power. The Second was a result of the Hyksos invading the Delta and occupying it for a century while the south squabbled with itself. The Third came as a northern regional leader and the High Priest of Amun in the south made themselves de facto rulers, reducing the office of pharaoh to a mere figurehead. Then in the first millenium BC, Egypt was conquered by the Assyrians, then the Persians twice, then Alexander the Great, which ended native Egyptian rule for centuries.

Now, the more interesting question is why do we still see ancient Egypt as encompassing a single, continuous state lasting 3000 years. I think the answer is because throughout all of those upheavals, the society and culture remained largely unchanged. While there were of course advancements and cultural evolution, the Egyptians were very conservative and viewed the maintenance of the status quo as essential to ma'at, the Egyptian concept of truth, justice, harmony, and cosmic and social order. A prime exanple of this resistance to change is the language; I can personally verify that Old Egyptian, the phase of Egyptian used in the Old Kingdom, and Late Egyptian, used from the New Kingdom to the Ptolemaic period, are as similar as Shakespearean and modern English, which are separated by 500 years, despite being thousands of years apart. The pharaoh, as the living representation of the gods on earth, was seen as essential in this worldview. So, everytime the state recovered after collapse, instead of starting over and developing a new system, they stuck to the model of their predecessors with maybe a few little tweaks. Even when they were governed by foreign powers, the Egyptians' rulers knew how important this continuity was for them, so they played along and tried to just insert themselves into the old system instead of just imposing their rule directly (they weren't always successful at being seen as legitimate pharaohs but that's besides the point). It isn't until the annexation of Egypt by jack booted Nazi thugs (Romans) that this changed. Despite the Emporer's name being used in temple inscriptions as though he was a pharaoh, it was clear that things were different since they were ruled by a distant Emporer instead of a local king and were forced to comply with the Roman Empire's model of bureaucratic governance. That is why, even though the culture in Egypt in the Ptolemaic and Roman periods was very similar, many Egyptologists see the death of Cleopatra as the end of ancient Egypt.