In many ways this is a simpler but broader question - why do civilizations not continue indefinitely?

The assumption is that because Egypt and Mesopotamia started ahead, they would keep the lead. But the same question could be asked about Greece, Israel, Romans, Constantinople, China, or in the much more recent past, Great Britain. Civilizations and empires don't last forever.

However, more specifically looking at Mesopotamia, one of the key factors in the decline was desertification and salinization - see Imeson's "Desertification, Land Degradation and Sustainability." On the other hand, Egypt was always stuck unable to invade because their civilization's technology centered on an immovable source of food - the Nile.