However, even in 1911 the Qing might have survived-- the commanders of the Beiyang Army ("Northern Army"), who controlled most of north China between them, did not initially join the southern uprising. However, the commanders (most of whom regarded each other as colleagues, and who had once studied together in the same schools) mostly decided that, rather than throwing China into civil war and weakening it further, it would be more effective to negotiate with the rebels. It was the resulting negotiation that led to the Qing being deposed-- a negotiation that was, depending on one's perspective, born out of nationalism of a kind.
Yuan Shikai sided with the rebels by his fear of irrelevance if the uprising was crushed. The Republicans and revolutionaries had infiltrated the New Army already. If 1911 was put down, you would have had Yuan Shikai overthrow the Qing himself while the Republicans and revolutionaries regroup, or even a new monarchy base around wither a Ming, or a descendant of Confucius.
There is just too much factional tension and incompetence to save the Qing at this point.