Typically, any political system (empire or not) eventually collapses, which several people explained below but without answer the question. There are several reasons for this, though this is probably not an exhaustive list.
1). Most empires, regardless of the tribute system supporting them, were agriculturally reliant. Through most of human history, there have been numerous bad harvests which promote plagues and movements of large numbers of people from agricultural production. Very few political systems of a complex nature can survive these problems. This is well-detailed in the monograph Plagues and Peoples by William H. McNeil.
2). Empires invariably seem to reach a state of stagnation where their political leaders become complacent and reliant upon their previous successes and prior strategies for dealing with problems. In Arnold Toynbee’s classic work A Study of History, he strongly makes the argument that its this inflexibility and complacency that causes empires to fall to their neighbors eventually, or to a new dynasty that is more willing to be innovative in finding solutions to the problems that beset the polity. Often this stagnation results in a failure to adapt the economy or distribution of resources in a way that will maintain the empire. We see this is in the debasement of the Roman currency, its over-reliance on foreign military forces, and its over-expansion. The Romans failed to adapt successfully as their world changed and empire expanded.
3). Since you ask specifically about empires, the greatest challenge for many empires is multi-culturalism. Several empires have failed due to an inability to maintain proper respect for the various cultures within that empire. We see this with the fall of the Assyrian Empire, destroyed due to its disrespect for and brutality against subject peoples, and with the fall of the Ming dynasty to the Qing who brought the grievances of an ethnic minority into an alliance with Han Chinese elements who had lost their loyalty to the Ming.
4). Sometimes empires over-expand as well. The collapse of the British Empire and the conquests of Alexander the Great could be attributed to this as well. Both these empires took on more territory than they could control effectively, with Alexander managing to himself following his soldiers desire to cease and return home and the British Empire failing to address issues of multiculturalism with its efforts to maintain hegemonic control requiring a vast expenditure of wealth and resources which the British population was no longer willing to provide following WWII
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