NB: I've separated the objective facts from my own derived conclusions for the sake of transparency.
Here's a summary of the numbers as I know them:^1
| Time Period | Date Range | Duration (in Years) |
|---|---|---|
| Early Dynastic | (ca 3,200 – ca 2,686 BCE) | 514 |
| Old Kingdom | (ca 2,686 – ca 2,160 BCE) | 526 |
| First Intermediate Period | (ca 2,160 – ca 2,055 BCE) | 105 |
| Middle Kingdom | (ca 2,055 – ca 1,650 BCE) | 405 |
| Second Intermediate Period | (ca 1,650 – ca 1,550 BCE) | 100 |
| New Kingdom | (ca 1,550 – 1,069 BCE) | 481 |
| Third Intermediate Period | (1,069 – 664 BCE) | 405 |
| Late Period | (664 – 332 BCE) | 332 |
| Ptolemaic Period | (332 – 30 BCE) | 302 |
| Roman Period | (30 BCE – 395 CE) | 425 |
| Late Antiquity | (395 – 639 CE) | 244 |
(I get 302 years for the Ptolemaic Period, but it just depends on when you start counting. Not a major difference.)
On the whole, periods of centralization generally lasted for several centuries, while periods of disunity were relatively short-lived. The Old, Middle, and New Kingdoms lasted between 400 and 500 years each. The First and Second Intermediate Periods lasted about one century, while the Third Intermediate Period was longer, but it was not truly a period of complete disunity. For much of that time, rule of the country was amicably divided between the High Priest of Amun in Thebes and a nominal pharaoh in the Delta, with the god Amun "ruling" the country and maintaining peace between earthly powers.^2
The takeaway is that the Ptolemaic Period was actually shorter than most periods of stability in Egyptian history. Five centuries was the norm. Rome explains both its longevity and its demise. It wasn't an autochthonous authority, so we shouldn't expect it to follow any trend perfectly.
Five centuries is roughly the amount of time that the benefits of centralization outweigh the costs. Bureaucracy is expensive, but it also has many benefits (freedom of movement and trade, reliable systems that everyone adheres to: calendars, laws, etc.). After around five centuries, skimming off the top (e.g. corruption, free riding, bloat) becomes so costly that it no longer makes sense to maintain the central authority. Local rulers chafe against what they see as oppression from the top without the corresponding benefits. They lobby for autonomy. Their people agree. The central authority gradually loses legitimacy until it crumbles.
Disunity provides a reset. But disunity has a cost as well. The most salient cost is trade barriers, but there are more everyday headaches that affect everyone. It's also "wasteful" in the sense that power and wealth are spread out when they might be concentrated, and ambitious local rulers can easily see this. After about a century, someone inevitably says, "Why don't I join it all together so that I can sit at the top of the heap?" There's a war of reunification. A new, leaner, central government is formed.
Rinse and repeat. This generalization is obviously not specific to Egypt.