There are, I think, a number of flawed assumptions behind this question, none of which make it illegitimate or a bad question to ask, but which do mean that I don't believe I can answer it as phrased. Let me break it down a bit.
The problem with the concept of 'modernisation' is that its definition is entirely arbitrary and circular. Polities/societies/cultures claim to possess characteristics of 'modernity', and in turn use the basis of their own self-defined 'modernity' as the litmus test against which they determine the degree of 'modernity' possessed by other polities/societies/cultures. In recent times the chief claimants of 'modernity' have been European polities and their settler-colonies such as the United States, Canada, and Australia, and it is by their standards that we conceive of 'modernity' as implying certain vague notions of technological ubiquity and the possession of certain but undefined institutions and social structures. On one level, then, being 'modern' really means being like 'the West' (however understood), but also in arbitrary ways contingent on however Western societies or scholars define the characteristics of 'modernity' at any one time.
Moreover, attributions of 'modernity' or 'advancement' or what have you are not just value-neutral designations. The way these terms are used implies some qualitative superiority to those who possess these qualities over those who do not, or who possess more of them over those who possess fewer. For more I'd urge you to take a look at this very recent thread with contributions by /u/Iphikrates and /u/DanKensington that further deconstruct the issue, but in short, the notion that 'modernity' is a good thing is in itself a subjective position.
On some level, the Qing might never be considered 'modern' whatever they did because the goalposts can shift so often and so easily. Let's imagine that they had introduced industrial manufacturing technology in a few major cities. Would we consider that conditions for 'modernity' had been fulfilled? Or would we demand that the quantity of industrial machinery needed to reach a certain threshold? Or that there should be a minimum proportion of cities with manufacturing industry? Or would we say that it's not just about industry or not about industry at all, but some vague notion of cultural 'modernity'? You can see why the concept is fundamentally useless.
So when we say the Qing 'failed to modernise', we're not saying anything meaningful. We're just saying that our arbitrary criteria for an arbitrary concept have not been met, and that therefore the Qing lacked some quality of 'goodness' which is so only by arbitrary designation.
That being said, it's far from useless to look at how the Qing compare to other major Eurasian state formations and consider their similarities and differences without resorting to moralistic value judgements. An incredibly fruitful route of enquiry has emerged out of the examination of the Qing's congruities with states such as Bourbon France, Muscovy-Russia, and the Ottoman Empire, considering two principal aspects:
Technologies and ideas directly imported from European states and applied by the Qing to similar ends; and
Tendencies towards similar sorts of actions in response to similar sorts of conditions.
Laura Hostetler's Qing Colonial Enterprise highlights cases of each: in the eighteenth century, the Qing sought to strengthen and assert their political authority (just like other successful Early Modern states in Eurasia), especially in upland regions of primarily non-Han indigenous settlement. To this end, they made use of Jesuit expertise in replicating European-style scale cartography, while also developing increasingly detailed ethnographic albums on their own initiative, paralleling efforts at ethnic classification undertaken by European colonial powers in the Americas. Peter Perdue, in China Marches West, stresses how the logistical demands of the early eighteenth century Zunghar wars drove Qing state development and led to institutions of increased state power such as the Grand Council and palace memorial system, paralleling the 'military revolution' and growth of 'fiscal-military states' in Early Modern Europe. In recent years, as the notion of 'fiscal-military states' has fallen out of vogue in favour of 'contractor states' in studies of Early Modern Europe, studies of Qing logistics by Dai Yingcong and Ulrich Theobald have reached similar conclusions and found the Qing to have also relied on similar mechanisms to translate financial resources to military power well into the 1770s and beyond. The general consensus is that by and large, the Qing were, at least qualitatively, entirely comparable to any contemporaneous European or Middle Eastern power (though there is an (in my view convincing) argument to be made for a considerable and widening disparity in the quantitative level of fiscal power.)
Now, as you may have noticed there, the scholarship I've been citing has all been focussed on the eighteenth-century Qing. How, then, did the Qing fall behind in the nineteenth century? Well, any number of explanations can be cited, but I think the more interesting and important point to be made is that they did not refuse to catch up, and that the Qing did not enter a permanent phase of divergent development from the rest of Eurasia. There is a growing body of scholarship that argues, for instance, that the Qing acted as an imperial power in entirely comparable ways to European states and Japan: Kirk Larsen and Bradley Camp Davis have argued that the Qing operated on a near-identical basis to their imperial rivals in Korea and Vietnam, respectively; Eric Schluessel has highlighted Han Chinese settler-colonialism in Xinjiang; a number of Chinese historians, whose work has been compiled and translated in the volume China: How the Empire Fell, have produced revisionist approaches to the Qing 'New Policies' post-1900 that have argued that these reforms were by and large successful.
So hang on, if I'm here arguing the Qing did not resist reform, then why do we think they did? I will suggest (non-exhaustively) a few explanations.
Our assessment of the failure of Qing reform efforts tends to be based on three major points of largely military failure in the last two decades of the empire: the defeat to Japan in 1894-5, the Boxer Uprising in 1900, and the fall of the Qing in 1911. But these failures for me illustrate the very problem of goalpost-shifting I highlighted earlier.
Firstly, considering the Sino-Japanese War and the Boxer conflict, there is no reason why military success in particular ought to be our primary metric of assessing modernity. Secondly, in these cases the Qing army was improved over what it was previously. The Qing in 1894 did possess a relatively modernised army corps in the Huai Army, and one of the most powerful on-paper fleets in Asia in the form of the Beiyang Fleet (with a combined tonnage of over 33,000t). Western officers during the Boxer war regarded Qing regulars as well-trained and well-equipped, and a genuinely threatening opponent. Setting aside the specific causes of Qing defeat (which in both wars had much to do with a mixture of poor officership and political division), what ought to be made clear is that the Qing did engage in military reform. What's happened is a conflation of a failure of reform – i.e., that the Qing armed forces had not improved sufficiently to win these conflicts – with a failure to reform – that is, that the Qing didn't even try.
1911 is an altogether thornier issue that I will elaborate more on in a subsequent sectioon, but the key point to make is that after 1900, huge strides were made in military and political reform, with an aim to eventually establish a constitutional monarchy with elected representative and advisory bodies. It was in response to the execution of some of these policies – particularly surrounding the membership and role of government bodies and the issue of foreign rail investments – that the revolution of 1911 broke out. Again, it was the failure of the Qing reforms that mattered, not the Qing's refusal to attempt them.