Empires like the Gökturk, Seljuk, and Mongol Khaganates explode into large realms in lightning-fast timeframes, often in 30 years or less. However, they all lasted for seemingly brief periods of time, often shorter than 100 years, while similarly grand sedentary empires like the Han dynasty, the Ming dynasty, the Ottoman Empire, the Russian Empire, and the Roman Empire all lasted upwards of 200 years. Some sedentary Empires like the Frankish Empire had a similar supernova-like existence, but they seem to be the exception rather than the rule. Why do Nomad empires come into existence and disappear so quickly?
I can only speak for the Mongols, though from what I understand, much of what I say will be mostly applicable to other similar empires and nomadic confederations.
While there a number of arguments to be made about the longevity of such states, in terms of why they break down I believe the most convincing arguments relates to succession matters, or more specifically, the failure to properly define a succession process to the Khaan.
You noted the speed in which many of these polities form, and I think that is particularly relevant to this matter. Especially for the Mongols, we see them go from a collection of tribes, to under Temujin in the late 12th century into a tribal union, and then in 1206 into an empire, Temujin taking the name Chinggis Khan (Genghis Khan). Within 40 years, this empire is stretching across all of Eurasia. 10 years after that, it has split into 4 (or 5, or even 6, depending how your counting) independent Khanates, at best only offering nominal allegiance to the Great Khan. That's a very quick timeframe, and you can argue that the Mongol Empire was in many ways a steppe nomadic confederation with imperial trappings (though not as applicable to the Yuan or Ilkhanate successor states), and many steppe customs continue in modified form under the yeke Monghul ulus.
One such custom relates to succession. For the steppe nomads, upon the death of the father, his belongings, herds and wives would be spread among his offspring, brothers or cousins. For the Mongols, the youngest son, known as the Otchigen, would be the designated individual for this often. There is generally no single designated 'successor,' to the father though, if he were a tribal chieftain or Khan. His successor would be decided via quriltai, a meeting of the families/clans/tribes to choose whomever was considered the strongest candidate. This could mean a very rapid shift in power balances within the society, alliances breaking, families being forced to lose everything (as Temujin's did after the death of his father, Yesugei).
The problem for the Mongols was that they kept this practice for their succession at the imperial level, which quickly proved troublesome. Chinggis' authority was so great he appointed his third son, Ogedai, to succeed him, seeing him as the most capable of his sons (or at least, the one least likely to start a war with his brothers). The idea of challenging Chinggis' own choice would have been near unthinkable (though some argue there were those who wanted Chinggis' youngest son Tolui to succeed him). However, while it seemed the succession to the position of Great Khan was now limited to Chinggis' sons and their descendants (with exception to descendants of his eldest, Jochi, whose paternity was uncertain, and in the late 1240s Chinggis' sole surviving brother Temuge Otchigen made an attempt to become Khan) it was not defined how that successor should have been chosen. Ogedai's descendants made the argument that the Khaghanate should remain within the line of Ogedai, but even after Ogedai's death his widow Torogene needed four years to persuade the other Chinggisids to elect her son Guyuk. Guyuk reigned for only two years, and after a brief regency by Guyuk's widow, the position of Great Khan was taken by Mongke, Guyuk's cousin, a son of Chinggis' youngest son Tolui. This 'Toluid Revolution,' was followed with a slaughtering of Ogedai's line, and later historians struggled to find excuse for Mongke taking power, writing Chinggis as giving 'clauses' for the throne to be taken by another branch of the family, or dropping 'hints' that Tolui's line should eventually take over. These are unlikely, but the vagueness of the succession made these things possible. Tensions over this legitimacy would form cracks in the empire.
The clarification of 'strongest candidate,' was alarmingly vague, and tended to lean to 'whoever had the strongest army,' Upon Mongke's death in 1259, two of his brothers, Ariq Boke and Kublai, both declared themselves Khan. Instead of a proper election, after a four year civil war, Kublai overcame his brother, but this conflict effectively broke apart the empire. It allowed other bubbling tensions to rise to the surface as branches of the family declared for one party or another, or began fighting one another over territory. By 1264, Kublai only directly ruled in Mongolia and China, the other Khanates recognizing his authority largely in name only, though he held influence.
Kublai would make efforts to appoint a designated heir (who predeceased him), but such a custom never took off among the successor Khanates. Without a proper designated heir, each succession was open to dispute, each time providing an excuse for internal conflicts to rear their heads and threaten the empire. In theory, the election of candidate should have allowed the strongest, most respected and capable individual to take control, but in practice it provided an opportunity for power grabbing and scheming.
In short, the succession procedures, or rather lack thereof, basically gave the Mongol Empire a built-in 'self implosion device.' While it could allow for strong candidates and successors (an argument for this elective process would be that primogeniture and similar successions can lead to a young child succeeding to the throne: not useful for military states like the Mongols), like Mongke and Kublai, such matters were more often were solved through shedding the blood of your relations than not.
See Timothy May The Mongol Conquest in World History or his recent The Mongol Empire for more on these matters in the wider history of the empire, as well as the other internal issues which augmented these breakdowns.