Examples: Egypt, Greek, Rome, Mongol, Spain, UK, Russia? It does not look like any of these will make a come back any time soon. I am not an historian so there are probably exceptions. Why what seems like a general trend?
There is no single common trend between the final decline of these empires. Egypt and Rome were conquered and replaced by foreign states; Britain and Spain's colonial holding gradually seceded. Egypt was an incorporated province after its self-ruled "empire" fell, Western Rome became divided into new various new polities, and Spain just shrank and retained its independence.
But the end of these groups' "rules" was rarely the first decline. In Egypt, historians refer to a few periods as "Intermediate Periods." During these times, multiple people claimed the throne, the centralized monarchy dissolved, and occasionally different parts of Egypt were separate kingdoms. But eventually one royal family would regain control. Many later pharaohs inscriped a king list in their temples- Ramses II's names every pharaoh until the first dynasties, but leaves out the dubious rulers of the intermediate periods and those of the Amarna period. This suggests some ideal of continuity that bridges the troublesome times.
In Rome's case, the middle of the 3rd century was a complete mess. The empire had seen turbulent competitipns for the imperium before (4 different dudes ruled in AD 69), but nothing like this. It was decades of incompotent child rulers, military coups, and incredibly brief reigns. At the end of the century though, Emperor Diocletian instituted reforms that would keep the Western empire around for 150 more years, and the Eastern half for another several centuries.
Or look at China. The Han Dynasty ruled the region for 400 years starting in the 2^nd c BC. The following centuries are called the Sic Dynasties period, when the empire dissolved into numerous states, many under foreign rule. But in 581, the Sui Dynasty managed to reunify China.
So contrary to your assumption, these grand states did decline and were able to come back.
Not true at all, though recoveries of empires are rare.
As an example in the Hittite empire lost most of it's territory, then an emperor named Tudhaliya I recoquored a lot of it and started a re-invigoration of the empire. Then it lost the territory again, then Suppiluliuma I led another recovery.