In lots of times in history, nomadic people/ horse archers beat up settled peoples. Mongols in China and Europe, Huns in Europe, etc... What led to their decline?
You've stumbled upon a rather generally accepted concept, though not a hugely precisely-codified one, that has been part of the study of Eurasian military history for some time, and that is what is sometimes termed the Nomadic Military Advantage (henceforth NMA). This answer of mine covers its core precepts in moderate detail, but to state again some of the key points in brief, bullet-point form:
The erosion of the NMA that you have observed arguably involves two stages: firstly, nomadic armies had to become sufficiently non-competitive that they no longer dominated in sedentary terrain; secondly, sedentary polities had to develop the capacity to overcome the nomads' advantages on their own turf. However, there are some shared features between the two.
Firstly, we may question whether even the Mongols were a 'pure' expression of NMA. Not that the Mongols themselves were somehow not nomads, but rather that one key factor in their ability to expand so far past the largely steppe and steppe-adjacent bounds of prior Eurasia-spanning entities like the Göktürks was their adoption of sedentary polities' siege technology. While the jury is still out on the Mongols' use of gunpowder in Europe and the Middle East around the 1240s, they were no doubt making significant use of the mechanical expertise of Chinese and Iranian siege engineers, and were definitely employing firearms in northern China by the 1280s (and so presumably must have been making use of single-use gunpowder devices even before). These technologies, which would go on to herald the ascendancy of the sedentary empires, first burst onto the world stage in nomadic hands.
But setting the specifics of siegecraft aside, it is also worth noting that the Mongol campaigns show the limits of the NMA in another crucial way, and for that we ought to look at the one great failure of the (nominally still-unified) Mongol Empire, that being the wars between the Mamluk Sultanate (based in Egypt) and the Mongol Ilkhanate (based in Iran) between 1260 and 1312. The Mamluks themselves, enslaved soldiers of various amirs, were very similar to the Mongols: they were usually either Central Asian or Caucasian in origin, and fought as horse archers. But the Mamluks had better horses, better armour, better weapons, and specialised military training. The Mamluks won most of the major battles in these conflicts, including the arguably decisive engagement at Ayn Jalut in 1260, where roughly equal numbers of Mamluks and Mongols plus allies faced each other, and where the Mamluks utterly routed the Mongols. Now, to be fair, this was not an entirely 'fair' fight, because the death of Möngke khagan in summer 1259 had led to the Ilkhanate diverting much of its Syria-bound invasion force to what is now Azerbaijan in preparation for a civil war with the Jochids (the 'Golden Horde').
So what is the limitation I'm referring to? Well, it's the fact that the nomadic style of warfare can be not only appropriated, but refined by sedentary powers. How and why is this?
The Eurasian steppe ultimately imposes limits on how many nomads can actually be sustained in it. Nomadically-herded livestock largely cannot become more efficient as a food source with improvements in technology. Technological advancement does, however, substantially increase the productive capacity of sedentary societies, though with the tradeoff of requiring increasingly specialised and sustained labour, which limits how much manpower can reasonably be split off from the productive labour force. What this means is that in most cases, sedentary societies designate a particular segment of the population for warfare, far smaller than what nomads can devote, but which receives a considerable investment from an ever-growing pool of resources. In addition, while this is by no means an inherent or linear process, states tended to become increasingly effective at extracting from that resource pool in order to wage war. This means that over time, sedentary states have been able to mobilise larger portions of a bigger economy towards warfare, while nomads hit a plateau pretty early – a plateau that was at one point much higher than what states could achieve, but which states had the potential to surpass.
The Mamluks demonstrate this dynamic quite well. Wealthy amirs gained resources through being the petty rulers of fiefdoms within the Sultanate. They used the resources gained from this to obtain enslaved Central Asians and Caucasians, and then funnelled further resources into their training, equipment, and upkeep, thus producing troops that could, mano-a-mano, out-Mongol the Mongols. Now, in 1260 the ongoing fragmentation of the Mongol khanate had created circumstances to mitigate the numerical advantage that the Mongols might otherwise have had, so we ought not to read too far into the Mamluks. Rather than demonstrating an emergent superiority of the sedentary state as of 1260, the Mamluks' success was more a sign of things to come.
As the late Medieval transitioned into the Early Modern, we see the rise of hybrid armies, particularly in the Middle East, where cavalry on the tribal model operated alongside cores of sedentary infantry, and where much more developed fiscal and political instruments helped to integrate these forces more strongly into state leadership. Timur was arguably the most successful early adopter of this, but we can see similar developments in the so-called 'Gunpowder Empires' – the Ottoman, Safavid, and Mughal states (all linked with Timur – the first defeated by him, the second emerging from the ruins of his empire, the third ruled by his descendatns). The notion that these empires were built on and around gunpowder has been severely challenged in recent years, and while they did maintain trained musket and artillery corps, tribal-style cavalry remained a critical component of these empires' armies. (On the Mughals see this post by /u/MaharajadhirajaSawai)
These hybrid armies did not always find huge success, however, and nomads could still win considerable operational victories. Timur may have triumphed over the Golden Horde in the 1390s, but his descendant Babur was expelled from Samarkand by more traditionally nomadic Turco-Mongols under the Abu'l-Khayrids in 1501. The Khanate of Bukhara, ruled by the Abu'l-Khayrids until 1599 and from then on by the Toqay-Timurids, remained a consistent thorn in the side of the Safavids, having reconciled with the Timurids in northern India in the interim. States that did not fully adopt a hybrid model, like the Ming Empire in China, found themselves particularly hard done by: in the Tumu Crisis of 1449, the Zhengtong Emperor, having suffered a defeat while leading an army against the Oyirads, was captured on the retreat barely 100km from Beijing and held hostage for a year.
Yet even there, we see the sheer resource potential of sedentary states coming through. It is true that the Tumu Crisis was a potent demonstration of how the Ming could not really out-fight its nomadic enemies. It is also true that subsequently, the Ming proved unwilling to use economic and diplomatic means to secure allies on the steppe and to forestall attempts at consolidation and confederation. But their last resort option, what Arthur Waldron not unreasonably deems the end result of decades of policy failure, actually worked. The 'Nine Garrisons' system, which ended up producing the physical structure we now call the 'Great Wall of China', created a series of layered defences that eventually covered the entire northern frontier of China proper, from the Gansu Corridor to Manchuria. And after the last pieces of the semi-contiguous wall structure were finished, there was never again a successful, sustained nomadic incursion, either by the Oyirads or their erstwhile allies the Northern Yuan. It was, ultimately, revolt from within that brought down the Ming state and collapsed its frontier defences, and a hybrid army under the Qing, combining Manchu aristocratic heavy cavalry, Mongol tribal light horsemen, and Chinese and Korean infantry and gunners, which capitalised on this crisis.
One entity I haven't yet talked about is Russia, which also made use of both hybridisation and fortification in its eastward conquests. Aside from using Chinggisid elites as intermediaries with Turco-Mongol communities, the Russians of course had their Cossack allies to match the nomads, and also made use of fortifications, ranging from simple wooden palisades to bastioned forts. These lines of fortification, constructed roughly along what is now the Russian-Kazakh border, remained more or less steady until the mid-19th century. The extent of this effort was obviously far smaller than the Ming's, but that can be chalked down in part to less necessity due to far greater competence at diplomacy, in part to a far smaller amount of resources (as well as a longer frontier to cover), and just a matter of priorities.