Such major rebellions include the Taiping Heavenly Kingdom that rebelled against the Qing, The Boxer Rebellion and then finally the Sino-Japanese War?
The answer to this question is a long and complicated one, which I shall try to condense into as short an answer as possible.
Firstly, the Qing military had declined massively. The once-vaunted Banner Armies had become little more than a collection of titles, whose holders had barely any military obligations (nor money to purchase arms) to speak of. Up to three-quarters of the 'professional' Green Standard troops existed only on paper by 1850, and provincial militia were deliberately disorganised and disparate to prevent the arrogation of military power by men outside the civil and military command structures. On top of this, over a century of peace in comparative isolation had left the Qing's military technology woefully obsolete. At the start of the Taiping Rebellion in 1850, the most advanced weapons of local manufacture were matchlock muskets and jingals alongside cast-iron smoothbore cannon, at a time when Europeans had fully converted to percussion cap rifles (and the Prussians had already introduced the Dreyse breech-loader) and were beginning to introduce steel rifled artillery. On top of this, Western steamships were vastly more versatile than their sail-only Chinese counterparts. Not only that, but the aforementioned matchlocks were a relative rarity in the Qing armies, with most men simply armed with bamboo spears or (if lucky) a sword. Under those conditions, forces could simply waltz through Chinese territory and sweep aside whatever resistance could be mustered against them, no matter how numerically superior. The defeats in both of the Opium Wars can in many ways be ascribed chiefly to a military disadvantage.
Secondly, up until the 1860s (and even to some extent afterwards) the Qing had an amazingly arrogant position towards foreigners, effectively treating all other powers as second-class states, which did not help their case at a time of immense military weakness. British observers in Taiping territory found themselves far better received by the Taiping leaders (at least from 1858 onwards) compared to their treatment at the hands of the Imperial government. The First Opium War appears to have done little to shake the Qing's belief in their own place in the world – the lack of mention of it in Taiping propaganda suggests that the ordinary Chinese were not shaken, either – given their immense lack of tact in the run-up to the Second, even in the throes of the Taiping, Nian and Panthay Rebellions. Even in 1884, the Qing (in the event actually somewhat reasonably) believed themselves capable of fighting a proxy war against the French in Vietnam (ironically making use of the Black Flag Army, who had once declared themselves part of the Taiping) in 1884-5. Add to that their outdated fleet (made even more so by the fact that the French steamships were now also ironclads) and you get a recipe for disaster.
Thirdly, the Manchu Qing did little to integrate themselves with their Han Chinese subjects, massively worsening the consequences of ethnic nationalism. Even the relatively conciliatory Kangxi Emperor implicitly stated that the Chinese, although capable of being intellectual equals of the Manchus, were infrequently so, and were their physical inferiors across the board. The Manchus lived in their own walled sub-cities, separated from their Chinese subjects, essentially packaging themselves for slaughter, be it by the Taiping, who killed over 20,000 Manchus in Nanjing in 1853, or the Republicans and Nationalists, who massacred 10,000 in Wuchang in 1911. The fundamental distrust between people and state could only lead to severe internal strife, and although the Qing co-opting of the Boxers in 1899-1901 was a brief turn in the opposite direction, this anti-Manchu sentiment, as demonstrated by the atrocities of 1911, never went away.
Fourthly, the Qing Dynasty had become immensely corrupt (and in some cases remarkably inept) at most levels of government. On top of the aforementioned case of squandered money in the army in the 1850s, even the Qing's modern Beiyang Fleet was in shambles. In 1894, during the Sino Japanese-War, Ding Ruchang, the fleet's admiral, had pawned off a main gun from his flagship (although most of the time the guns were used for storing the sailors' lunches anyway), and at the Battle of the Yalu River, despite probable warning from his captain, ordered the remaining guns to be fired straight forwards, a decision which was to prove fatal for the Chinese fleet, as a crucial construction defect resulted in the shockwave destroying the flying bridge and knocking out the entire senior command. Not only that, even in their final years they were able to lose the backing of key senior leaders, the particular example being Yuan Shikai, who, heading China's largest modernised army, defected to the Revolutionaries in 1911.
Finally, this problem was compounded by the Qing's decision to prolong their lifespan by betraying their own principles and destroying their centralised government during the Taiping Rebellion. The Qing, like the dynasties before them, had tried to prevent the onset of regional autonomy by heavily restricting their generals and civil servants. Hence, they were not allowed to serve in their home provinces, but were required to go into prolonged periods of official mourning upon the death of a parent, during which time they were thus out of office, and regional militia were not allowed to be coordinated, so that the leaders mobilising them did not gain more power than their own individual wallets could afford. However, they approved entirely of the Hunanese Zeng Guofan's plan to raise an army in Hunan, whose members were appointed by personal connection from Zeng's immediate subordinates down to the rank and file, and indeed funded all of its operations from the imperial purse. Whilst Zeng tried (and failed) to take the Cincinnatus approach from then on, his protégés Li Hongzhang and Zuo Zongtang exploited their temporary monopolies on military power for personal gain, such as through being the collectors of the Lijin tax, and setting the precedent for the Warlords of the post-1911 period.
Essentially, the Qing started out in a bad position, and everything they did in reaction to their enemies exploiting said position generally made things worse, or at least failed to make things better. In destroying the Taiping, their most severe existential threat, the Qing signed their own death warrants by empowering the warlords. In trying to modernise after their losses in the Opium Wars, they opened up further avenues for corruption. The one exception is foreign policy, where the Qing essentially followed an immensely arrogant course of action for virtually all of their existence.
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