The Han period was of monumental importance for the Chinese history, and as a testament to that era the majority ethnic group in China to this day see themselves and call themselves the Children of Han.
One of the major factors in the fall of the Han Dynasty was corruption, and as the Han court grew weaker and got more distant from the local population corruption rained supreme.
The other reason is taxation. The government did not have money to sustain itself and many nobles were exempt for the taxation and the peasants would run and hide from the tax collectors, making the task of collecting taxes extremely difficult. There were other outside forces too and many more internal ones also.