Like the fall of the Roman empire has a few contributing factors, so does the fall of the Qing dynasty.
Remotely, the Qing dynasty was militarily weak in the 19th century. It had lost the Opium Wars. It lost to Japan in 1895 and was invaded by the Eight Nation Alliance in 1900 to put down the Boxer rebellion; the British also leased Hong Kong about this time. Governmentally, there was a coup in 1898, revealing instability, and the (imprisoned) Emperor and the Empress Regent died practically simultaneously in 1908, leaving a child emperor and a relatively weak regent.
This was a rough period: the Chinese Martyrs canonized by JP2 are from this time, and the Eight Nation Alliance looted Beijing and raped women, something the Chinese still remember.
Proximately, the dynasty was stuck with a payment for losing to the Eight Nation Alliance and tried to manage it by nationalizing the railway and putting it under foreign control, which led to several regional uprisings (supported by anti-Qing exiles as well as the Black Dragon Society of Japan) that the dynasty was too weak to control.