The short and obvious answer is that 2000 years is a very long time in which many things can happen. Despite what geographical determinists like Jared Diamond will tell you, there is nothing innate about any region in the world that gives it a permanent advantage in prosperity, stability, or exploitable resources. Empires and centres of learning rise and fall. This has been a subject of fascination since antiquity itself, and arguably one of the main reasons why humans are interested in history:

For many states that were once great have now become small; and those that were great in my time were small before. Knowing therefore that human prosperity never continues in the same place, I shall mention both alike.

-- Herodotos, Histories 1.5.4 (late 5th century BC)

The longer answer would involve an extensive history of both Egypt and Greece from antiquity to the present day, which is an unreasonable thing to ask of a humble redditor like me. But the fundamental point in both cases is that all parts of the world, no matter how rich and powerful (or alternatively, how remote) are affected by internal crises, external influences, and chance events. The greater the span of history you're looking at, the more of these you will find. It is therefore unsurprising that no single part of the world has ever managed to maintain a significant relative advantage over other regions in either military-political power or cultural and technological innovation for more than a few centuries at a time.

It's important to stress the word "relative" in that sentence, though. A lot of the time, states don't actually experience some dramatic collapse, but are either overtaken by rivals or simply forced to accept the emergence of peers. Egypt, for instance, always remained one of the richest and most populous parts of the ancient world, but its initial dominance was first checked and then superseded by its neighbours in Mesopotamia and Kush. Egypt would eventually become one of the wealthiest and most strategically important parts of empires more powerful than its own had ever been (Assyria, Persia, Rome). Once other powers had reached similar levels of urbanisation and cultural attainment, Egypt became relatively less prominent even if its own vitality did not diminish.

The Greek world was never a superpower in the same way; it was never politically united and never acted on the world as a single entity. It rarely had much political or military power (with a few short-lived periods of exception) and its economic and cultural influence is often overestimated due to chance survival of evidence. Even so, again, the autonomy and prosperity of the states in this region was first rivalled and then superseded by Macedon and then by Rome. Once these states had taken over, mainland Greece could not regain a lasting political independence (despite constant efforts), and instead became a region for others to fight over. While many city-states initially flourished due to the relative peace that Roman domination brought, the archaeological record shows an eventual and largely irreversible decline in population, wealth, and cultural output. Part of this decline was no doubt driven by the greater scale and interconnectivity of the world of the Hellenistic kingdoms and the Roman empire: Greeks poured out of the old heartland and moved all over the Mediterranean world and beyond. But part of it was simply that the centres of wealth and power, and the crucial nodes in the trade network, had shifted away over time.

Once a region like Egypt or old Greece enters such a period of relative political and economic irrelevance, it is very difficult to regain prominence, especially if the new powers of the world treat these regions as exploitable. Both Egypt and Greece had times in later history when they were centres of power and intellectual prestige, but neither would ever regain the relative level of wealth and power they had in the periods for which they are famous.