The Qing did reform. The issue is that they lost political support from necessary elements (military, literati, non-royal elites, etc.) of the population even as the majority of the Chinese population likely supported them to the end. Unpopular reforms actually contributed to the loss of political support along with constant humiliation at the hands of Western powers (and eventually Japan).
Another possibly less important factor was the rise of a more European-style Han nationalism among the literati as resistance to the Qing became less about restoring the Ming and more about restoring Han leadership to the Han nation. And in response to the rising nationalism, unlike in many European countries, the royal family did not force themselves to adopt the ethnic traits of the majority group. In fact they did the opposite, quixotically clinging to their Manchu identity even as they had essentially become Han-ized. The alien royal family became an obvious target for revolutionaries like the Taiping and the Revive China Society.
Ultimately it was possible for the Qing to carry on for some more time than they did IOTL. If the Xinhai Revolution were viewed as more of a threat by Western powers, they would help crush it like they did the Taiping decades before. But a Qing surviving in such a way would merely shamble onward as a zombie-state, propped up by Western imperialists for the interests of themselves. Eventually a rebellion would succeed and the Qing would be toppled.
IMO in order to avoid being overthrow and be in a position to continue their program of reform, the Qing must succeed in resisting Western imperialism or, at the very least, avoid the string of humiliating defeats that occurred IOTL.