Why did the Frankish Empire not last long?

During the reign of Charlemagne, the Frankish Empire was able to reach the peak of its power. However, after his death, the empire is weakened. In 843, the Treaty of Verdun was signed between the heirs, which meant the division of the empire into three parts. We can say that the ambitions and aspirations of the heirs to rule alone became the main reason for the collapse of a large empire, as well as the reason for its decline and weakening.